Kashmir for One, instead of being cease fired due to Nehru's insistence on UN is stopped, instead India takes over all of Kashmir.
Maybe. But further war would be difficult( yes really not that it is discussed widely) as the next logical offensive would have to be towards Mirpur from Jammu and a minor thrust from Poonch and with no proper roads the Poonchi front would be difficult to support and the offensive from Jammu would have to cross multiple rivers opposed and increasingly defended by Pakistan Army, which was finally getting it's organization right. Taking back Mirpur would be bloody and then one would have to proceed all the way through the heavily defended mountains to Muzaffarabad, which would result in highly disproportionate casualties among the Indian forces and the location means that Pakistan can sit behind defensive terrain and have shorter supply lines unlike India which was has to haul everything on Truck on unpaved roads and mule back from Jammu. And even Jawahar Tunnel wasn't there so another winter lost.
GIlgit Baltistan presented the same problem, the Gilgit Scouts were an elite unit and were beaten because of the overstretch and by the time India took back Kargil, the supplies were used up in the offensive and months of resupply would be needed before they could launch another offensive towards Skardu, again along mule tracks, not even roads and aerial supply would be needed which was scarcely available given the airlift capacity needed to sustain operation in the Kashmir valley. And only route to get into Gilgit Baltistan from India was through Kargil(which also supported the route to Leh as the road via Manali wasn't there) which would make holding both Gilgit Baltistan and Ladakh a nighmare unlike Pakistan which could easily access it and use routes maintained by the British Indian Army connecting the North West Frontier Province to Gilgit.
And finally Gilgit Baltistan was leased by Kashmir to the British and not ruled directly which brings in legal problems and the closest analogy maybe the erstwhile Berar province.
The ceasefire was requested due to several reasons not whims.
drastically different policies of India, especially concerned to Foreign Policy.
It would be different but maybe not drastically different. It was a common view that India was too large to be an ally of a superpower or a mild satellite state even but India was weak enough to take care of its needs on its own. It was that combined with Nehru's idealism that took India to a non aligned position.
A possible major change if relations with Pakistan are repaired(Liaquat Ali Khan and Nehru supposedly reached an undisclosed deal in New Delhi during Liaquat Ali Khan's visit regarding Kashmir, that was shot down by Jinnah so a longer war continuing to after Jinnah's death would probably see a similar agreement reached) is that in the early 50s during the formation of SEATO Ceylon(Sri Lanka) wanted a conference to be held in Rangoon or Delhi to decide upon the future of Security in the sub-continent, possible plans being that the four countries (India, Pakistan, Burma, Ceylon) join the NATO or form a regional mutual defence pact. Nehru rejected that conference because of his idealism and opposition to military alliances in principle, we don't know the ramifications if such an alliance was really formed, maybe an earlier and more successful SAARC.
would he agree to annex nepal and Bhutan after the failure in Tibet to prevent Chinese influence in those regions?
No he never wanted something like that and Nepal,Bhutan and Sikkim were loyal puppets although India had minor territorial disputes with Nepal India could give away the Kalapani region which a logical interpretation of the Treaty of Sugauli makes it a part of Nepal and it has only three villages and is so small that one cannot notice it in a map, additionally Nepal has said that it would protect India's interests there by probably leasing the area to India and the only strategic reason to keep tat area being the present road there to Mansarover. Similarly the lease of the Tin Bigha Corridor to Bangladesh was immensely delayed. But the attitude to solving border disputes by not offering concessions doesn't work so India still has so many border disputes. China's initial offering of concessions solved many disputes like with Nepal, Burma and Laos and then Pakistan.
The threat that China poses to India may be recognised early and steps would definitely be taken to counter them but maybe he won't try to unilaterally define the border with China in Ladakh and present it as a fait accompli and may actually negotiate and with a Zhou Enlai like person negotiating on China's behalf a deal can be potentially reached. India never actually controlled the Aksai Chin or Pakistan the Shaksgam Valley, here if Giglit Baltistan is held the army is stretched thinner here and might no even make the nominal visits to Aksai Chin the reached settlement would definitely be better than the Line of Actual Control, with potential gains in the Pangong Lake and the Spanggur Tso sector for which negotiations failed as Krishna Menon considered the Chinese weak and asked for territories to be received first legally and militarily before India even withdraws troops for the areas it would vacate in return.
Sikkim was annexed on Indira Gandhi's whims and caused panic in Kathmandu and Thimpu, and India's self imposed big brother nature and arrogant attitude(Nehru led India was perceived to be arrogant at multiple conferences involving third word countries like the Bandung conference and the general arrogance and high handedness while dealing with Nepal Bhutan and Sikkim) didn't help. Even with Patel Tibet would be lost but probably India would not act in a way that makes China seem reasonable.
That's what I said, India would border Afghanistan and take all of Kashmir, which includes Gilgit Baltistan and Pakistan Azad Kashmir.
Not that we would notice any effect from that outcome. At the very least it would take a decade to a have a proper road to Gilgit, which from day one would be over used due to military requirements then another two decades before the roads get built to the Afghan border and the Wakhan corridor through unforgiving terrain and the roads would be closed during winters. The same problem is encountered in the Karakoram Highway today and trade between Pakistan and China is mostly by sea so no major problems.
Also, if India does simply waltz in and take over Kashmir it's reputation is going to tank internationally, even with an accession document but that probably won't change anything, since a couple of years later China is going to do the same thing.
But Patel was the one opposed to entering Kashmir untill and unless the Maharaja signed the Instrument of Accession, once Nehru got onboard with the idea he tried to delay the accession so that the intervention could be painted as a humanitarian crisis needing attention.
International reputation and goodwill did not bring India anything worthwhile.
It did, it maintained India's support from the third world countries, fair play and not trying to play the superpowers against each other and balance meant that the Europeans and the Eastern Bloc stood with India and was the reason that Nixon and Kissinger's hostility to India didn't result in economic sanctions in 1971. The goodwill acquired also prevented sanctions after the Liberation of Goa.
Most of world would quite simply not care or forget any wars soon, considering how many wars there were post WW2.
Not wars that attract attention like Korean Ear, India Pakistan wars, Arab Israeli wars, Falkland wars are all remembered due to the significance and the proxy game. Whereas the Uganda Tanzania war, the South African border war are forgotten due to their insignificance.
Would he implement a land reform though? This was the hubris of the Nehru administration that no centralized land reform was initiated, that led to wastage of water with primitive agricultural practices in large parts of India
He was an older generation who would have to bow down to these demands of the younger generation that demanded land reforms and his legacy as a consensus builder says that he would accept it. State governments were starting land reforms of their own initiative and it only makes sense that the Central Government follows suit.
Wastage of water and primitive agricultural practices cannot be blamed on the land reforms as they were prevalent even before. While one could argue that land fragmentation hindered the adoption of modern technologies but it cannot be argued that it brought down productivity or drove up wastage as the Green Revolution along with the land reforms increased productivity massively and Government subsidies rather increased the technological input into the land.
Also Soviet style 5 year plans where light and medium industry is developed in India with licensing agreements with the Soviets to export cheap manufactured goods to third world nations. This could be the basis for early industrialisation of India similar to Deng's China.
Indian consumer goods were superior to the Soviet ones and not particularly cheaper than western products so it couldn't compete in the Third world countries. Better economic policies would still encourage growth.
Companies need to be productive and get competitive within one's home country before going abroad successfully but socialism would still be there(Even the Eight Industrialists Plan for the economic development of India was remarkably socialist, when businessmen preach socialism, the society absolutely demands it) but in a softer way, which may help some businesses succeed and a slightly to moderately better economy.
China like industrialization can't be done in India as China lost faith in its system after the three devastating and stagnant decades unlike India where opinions about the economy widely varied and some were even fine with the British Indian economic system. China's growth was a result of several factors like the state of economy meant it was a clean slate, state ownership of land meant that infrastructure projects never faced hurdles like land acquisition and massive compensation to property owners, the social system which was preserved meant that opposition the government wasn't a big thing unlike India where opposition to the British Raj and Democracy meant that opposition was a real thing , the lack of a Cold War in the 90s where they received the US Industry on a plate and became the factory of the world.
we do know he was a conservative Hindu
Yes but he was a mordernist. Nehru wanted rapid and immediate reforms to the Hindu religion whereas Rajendra Prasad while recognising the need to modernise did not want a bill targeting a religion in particular and pushed for a Uniform Civil Code. Patel's position was between those two so we probably see a slower and maybe a slightly toned down series of bills modernizing the Hindu religion from the regressive state of affairs it was before.