if they weighted (fully) by float (perhaps the average float from the trailing 90 days to the re-balance) it would not be as easy to game. The Nasdaq is accounting for float, but not completely.
They are, but SpaceX is trying to get rules changed. They want the index to buy at a multiple of the float, so they release say 5% but get bought as if they had released 15% float. They also normally wouldn't be eligible for index inclusion for ~1 year, after showing multiple quarters of good stewardship, etc. They're trying to bypass all that
I don't know about the funds, but it's really about the index. Both for the index funds that use the index, and the active mutual funds and index funds benchmark to that index.