Sweden never takes Narva/the Ingermanland from Russia, giving the Empire a "Window to the West" much earlier.
Taking into an account that even few reigns after that "window" was open in OTL all cargo to and from Russia had been carried by the foreign ships, the main practical meaning of not losing Narva is that Tsardom of Moscow is not paying the custom dues to Sweden (export/import was going through Swedish-held Baltic ports). Due to the obvious fact that Sweden was economically interested in that arrangement and that the trade route through the White Sea ports (Kholmogory and then Arkhangelsk) was going on since the time of Ivan IV, a notion of the isolated Russian state is just one of the historic legends not supported by any facts.
Not that an absence of the ports prevented extensive contacts with "the West". There were numerous foreigners on the service of Ivan III, Ivan IV and the early Romanov tsars. Even before Peter I was born the Tsardom had a Western model troops trained and commanded by the foreign officers. At the beginning of his reign Peter traveled across Western Europe (and there are extensive records of him and his companions behaving like swine in the Netherlands and England
).
Ditto for the diplomatic contacts: besides obvious relations with its neighbors, Russia joined anti-Ottoman coalition in the Great Ottoman War.
Russia is able to therefore project power in the West much earlier
Sorry, but realistic projection of power started only during the 7YW or, optimistically, during the War of the Polish Succession. In both cases possession of the Baltic ports was not a critically important factor comparing to the land power.
The 1st important naval expedition happened only during the 1st Ottoman War of Catherine II.
and enter into favorable alliances earlier also, thus enabling them to crush the PLC much earlier (Probably around c. 1700 in the time period of the Great Northern War)
Actually, since the Russian-Polish War of 1654 - 67 the PLC (the part of it that was not conquered during that war) ceased to be a danger to the Russian state and after it was diplomatically forced to give up Kiev forever in exchange for the Russian participation in the anti-Ottoman war there was very little the Russian rulers wanted from it in the terms of a territory. As for the political influence, August of Saxony had been chosen with the help of the Russian diplomatic pressure (and financial backing) and by the end of the GNW the PLC started descending into a position of the Russian vassal state with Russia getting pretty much a free hand in Courland (formally, vassal of the PLC), defining PLC's succession and pretty much dictating the PLC internal policy. How exactly earlier possession of Narva would result in the earlier "schedule"? If "crushing" the PLC means "partitioning" (in the OTL prior to the 1st Partition it was as "crushed" politically as any formally independent state could be), the 1st Partition was actually a political defeat for Catherine II: parts of the Russian vassal state went to other Great Powers.
Now, what ARE the "favorable alliances"? There was a limited number of the potentially meaningful European partners and alliances with most of them were hardly "favorable" for Russia. What was "favorable" for Russia in being involved in the 7YW? Great expenses, big losses and the only
potential gain would be Eastern Prussia which Russian empire did not need and which it was
hoping to exchange for Courland in which it was already doing pretty much whatever it wanted: the Duke of Courland was sitting in an exile in Yaroslavl very happy that he was permitted to leave Siberia and even happier that he was not executed by quartering (according to the sentence of 1741) while the Duchy, with a graceful permission from St-Petersburg, was administered by his son.
As an ally against the Ottomans Austria proved to be rather a handicap during the wars of the XVIII century.
Prussia was an ally but the profit from this alliance was zero.
Close to the end of the XVIII there was Russian-French rapprochement but the main profitability for Russia was
official cessation of the French military help to the Ottomans (some of the French specialists in fortification and artillery still had been operating there unofficially) but militarily it was of a lesser significance than "self-inflicted wound" of having Potemkin as a commander-in-chief just because he wanted to get Order of St. George 1st class (with all his merits as a reformer, etc. as a high-ranking military commander he was a complete nincompoop).
Almost only "favorable" European alliance was with on with Britain, Russian main (and almost only) direct trade partner in the XVIII century. Besides having (by the reign of Catherine II) a positive trade balance with Britain, Russia was able to send a naval expedition to the Mediterranean using the British ports for repairs, getting supplies and even buying the new ships and the British naval officers for service in the Russian navy. Of course, during the Revolutionary-Napoleonic Wars the benefits turned into a huge disadvantage.
So which favorable alliances do you have in mind?
and have plenty of time to stabilize their control of the region before Napoleon's conquests ignite nationalism in the modern sense across Europe. However, the incorporation of Polish serfs--accustomed to much more liberty than their Muscovite counterparts--and resulting unrest as well as earlier exposure to the Enlightenment forces/enables an 18th century tsar(ina) to liberalize much more than IOTL Ekaterina II, in turn letting the Russian economy modernize much more quickly in the 19th century.
I don't even know where to start.
An idea of the "stabilization" of the PLC is a very interesting one but (a) occupation of its whole territory by the Russian empire is hardly ever considered, (b) as was demonstrated by the experience of the Russian-held "Kingdom of Poland", it was close to impossible to achieve "stabilization" in the terms of turning the population into the loyal Russian subjects (a noticeable part of it would still hope for the independence), (c) "stabilization" of the PLC without partitions/occupation would most probably mean anti-Russian arrangement even if just due to the existing perceptions and history of the vassal relations.
I'm not sure how exactly the serfs in the PLC had been enjoying any noticeable degree of a liberty: in a country where the serf-owners were not seriously restricted by any laws and did not pay too much of attention to what was passing for PLC's government, the rights of the serfs were not guaranteed by anything. An idea that the serfs unrest in the PLC is going to result in abandoning serfdom in Russia circa XVIII is plain silly, just as an idea that the Polish serfs were somehow exposed to the ideas of Enlightenment. If anything, Catherine II was as "enlightened" as it goes but after assembling a Grand Commission she easily found out that even merchants were in a support of the serfdom (providing they are also allowed to use serf labor) and ended up with "if I abolish the serfdom I'm going to be killed by the nobles before the peasants will come to save me".