Are you sure you're computing the basket correctly including cash component? For major ETFs like SPY or XLF they basically never trade away from NAV, not even by 0.01. HFTs are why. Authorized Participants can create/redeem in-kind at the end of the trading day. Borrow rates on individual stocks don't matter unless you're trying to put on a partial hedge and carry it. Most of the people playing this game have a market maker exemption and aren't concerned with shorts intraday.

This trade used to be extremely lucrative. I was there. It was awesome. Years ago the ETF and basket NAV would cross one another constantly and you could build a fully-hedged position for a profit if you were extremely fast. People still make money on it, but not as a pure speed arb. Like everything else, the fastest traders and those who execute best win. The fact that it's not as lucrative or easy anymore is indication that the markets have become so much more efficient.

Nope. For large liquid ETFs they are arbed so the values are in sync.