Well, SpaceX uses inconel. They also must have a quite good understanding of pyrotechnics, as they need to use that in a lot of places, eg. stage separation.
So I'd say yes, at least on the tech transfer part.
Inconel has been around for decades. It's just a nickel alloy. Nothing terribly special about that.
SpaceX seem to try pretty hard to avoid pyros -- one reason I've heard is that pyro devices can't be tested!
i believe they do still use a few, but pretty sure not for stage separation.
I don't think so. At least, it hasn't been publicly reported as far as I know. So although I'm not saying it's impossible, I'd be very interested to know the source for your statement?
Hopefully once they iron out the kinks in space travel they can release it to the Tesla with a software upgrade, or maybe an even better fuse!