How much concrete and other building material will you need for all of this. How many ships will you need to carry this all around africa until FNA and Sicily are taken.
Well, the British can always ship cement from India. In 1938, India produced 1,5 million tons of cement. Class A airfields need 18k tons of dry cement and trust me there is no need to ship aggragate as it is mined locally. I m pretty sure the Commonwealth can afford to send the material. No need to involve british cement. Moreover, in TTL there will no reason at all to develop heavy bomber airfields from scratch in Palestine to base USAAF B-24s.
Besides, I m pretty sure Tripoli will fall sooner than 23rd January 1943 (OTL). There will be no reason for the British to continue developing infrastructure in the Western Desert after Tripolitania is conquered.
So how many quaries are on Crete and how much can be dug from them each day.
Well, we can take a look at the actual history of occupied Crete. The german airfield at Tympaki was built from scratch with local materials and local (forced) labor. The airfields at Maleme, Rethymnon and Heraklion were expanded with local materials and labor. These airfields did not host heavy bombers, but hosted a significant part of the X. Fliegerkorps with twin-engined bombers and fighters.
If the Germans could do it, are the Allies incapable of doing the same thing? So, OTL shows that 4 supporting airfields that can host twin-engined bombers and fighters can be built without involving Britain and precious shipping. To build the infrastructure for a staging bombers (that will have the Delta as their main bases) is doable with additional help from the Commonwealth - the locals will have your fighter airfields built on their own.
So your following answer has been answered by OTL
How many additional airfields for the fighters and other planes to support the offence
Now that you know how much shipping you need, what are you going to give up to provide this shipping? How much less food or steel going to the UK? And remember how many months from UK to Crete and back via the cape. How many Canada - UK runs could be done at the same time ?
No less food for the UK compared to OTL. We have established that the airfields can be built without a single truckload of cement from Britain. All the rest needed for an airfield to operate (bombs, spares etc) were sent already in OTL to Western Desert, Delta and Palestine. The 98th Bombardment Group in Palestine in OTL had in any case to get its bombs from the States. Of course, in TTL you can still base the Group in 1942 in Palestine just for ... flying missions against empty desert.
Good chance of a slower build up for North Africa as some of the ships carrying what the army needs will now be for the RAF in Crete.
In TTL the Commonwealth is doing incredibly better in Libya. I really cannot see the Libyan Campaign getting prolonged as much as in OTL when the Axis have a single port and the British have Cyrenaica. Build up North Africa for ... what exactly?
No chance of any build up/resupply to Far east in 1941 as no spare ships if you building and supplying an air offence in 1941 from Crete.
I sincerely don't think that anybody suggested an air offensive from Crete during 1941.
What would make sense at an initial stage (second half of 1941) is to repair the existing airfields for fighters and the odd Swordfish squadron. The Far East can not be affected in any manner.
To the contrary, I suggested that the existing camps in Palestine are needed to house and retrain the surviving Greek Army. So, the Cavalry Division can go to an imperial backwater (e.g. Malaya) to transition to the 10th Armoured. Likewise, there is really no need for at least an infantry division (e.g 70th or an australian one) and it can be also send early on in Malaya.
After all, the East African Campaign is proceeding faster compared to OTL, curtesy of the infantry tanks in Sudan. As soon as Massawa falls, the 4th Indian can return in Egypt. Without the initial german success in Cyrenaica, the British can build an Army earlier than in OTL, freeing up units for other uses. This further supports sending the previously mentioned units at the Far East.