In order for APT to work, does it need arbitrageurs like LTCM to borrow almost infinite amount of capital to trade against mispricing and generate alpha?

No. If LTCM didn't borrow, arbitrage trading can also make price go back to fundamentals.

Yes. The reason is only because that LTCM wants to have higher return. It has nothing to do with APT assumptions.

Yes. With infinite amount of capital, arbitrageurs can have large enough power to push price back to fundamentals.

No. LTCM guys are just too greedy.