1. BTC/Alts rise because these are seen as alternative investment.
2. BTC/Alts fall because these are seen as an even more speculative asset than stocks.
3. Nothing happens
It is hard to answer definitely to your question
If it is ever possible at all. The main reason is that Bitcoin is still a rather niche financial instrument, thus it can come out any way. Indeed, Bitcoin is as speculative as most speculative stocks out there, but I still don't think we can measure it up with the same metric as stocks (i.e. most risky ones will fall the hardest). Basically, Bitcoin is a thing unto itself, and people heavily invested in stocks (like, say, Warren Buffett) are hardly interested in Bitcoin. So it could be the third option, but this is just not possible since everything is so interrelated and intertwined. Personally, I'm more inclined to think that if only the stock markets crash (and nothing beyond that), Bitcoin may actually gain in value (as well as alts)