A tarantula will not attack a cat; it will bite a cat if attacked by one though. Tarantulas are actually quite docile.
Only if provoked but if the tarantula is kept properly housed in a cage the cat can't get into or knock over, there shouldn't be a problem. For the most part, a tarantulas first defense is to run. Most won't attempt a bite unless the threat continues.
Yes it will and they are VERY fast. Had one as a pet in a cage before. I would not trust it around the cat. They have venomous fangs and they bite really hard. Saw it killing a mouse once and once the fangs are in, they do not let go so they could really hurt a cat.
if the cat provokes the spider then the odds are it will attack back.
If it feels threatened.