1a. Protecting tanks is not really important, but protecting vehicles (trucks) that every tank/mech division has inside them is worth considering. The trucks will be invaluable later on, to create tank/mech corps in 1942+ and fueling your offensives. Of course its a trade-off - risk them at the front right now, or save them for "later" - but will there be any "later" if you don't commit enough?
3. You might have pulled them into a region that is frozen as a whole, so the divisions get frozen as well. (And they don't let it go..) The most notable area early on is Finland, but maybe Bessarabia works like that as well if the Romanians are not active? I haven't tested it.
4. There are a lot of options, of course with pro's and cons. The most obvious con of every decision is the alternative cost to it. Replacing bad leaders is an option - especially in the most heated area - in MP games it is usually the Leningrad direction. If you want to place a good general, do it on the army level, the corps are disbanding soon(ish) - around Turn 5+. But if an army gets a nice leader, dont forget to disband all the corps underneath, or the effectiveness will be diminished. Other AP spending ideas include disbanding fortified zones, creating SU's (sappers most likely, though they got nerfed substantially), rearranging OOB (but with some experience you could minimize the cost here by retreating in an organized way - sticking armies and corps together - but some is always required), also pulling AA formations out of the cities (be careful, pull only the ones that are really close to the front - about 5 hexes, otherwise you can lose like 15 AP without any warning). A potential AP cost to pay is also in the SU rearrangement issue - if not using the automigration strats with locking/unlocking HQ's (the soviet side is really tricky though, arriving armies entering with unlocked status, so STAVKA sends them a lot of crap anyways if its unlocked itself).
5. I usually put all the airforce to reserve turn 1, so it is easier to manage and allocate in the following turns, some people deem it unhistorical/gamey, but it saves a lot of clicking, frustration and time, and I'm sure the AI won't mind. Every piece of equipment is worth saving, depending what you want to do later. Definitely recon planes are worth their weight in gold as you produce next to none. Bombers and attack planes are also quite important, but you will soon be producing enough. The most dispensable are the I-types fighters.