How likely do you think it is that we could permanently escape earth and survive/flourish?

Almost 100% likely. We're at the point where asteroids and comets pose almost no threat, because we're developing the tech to nudge them enough that they avoid Earth. We track all the big stuff, and should have years of notice to prevent global catastrophe. In just another 20 years, if a large asteroid/cometary impact hasn't happened, it never will. Nukes? Even if Trump starts some serious shit, there'd still be some survivors, somewhere. Billions might die, but a few tens or hundreds of million might live, if not more. Eventually, they rebuild civilization, and it probably doesn't take but another few thousand or ten thousand years at worst, the blink of an eye on astronomical timescales. Similar arguments for an epidemic, whatever. Some people, somewhere, survive and go into subsistence until they can rebuild society. And society always wants to eventually expand into space. If we can avoid the billions-of-deaths-thing, though, yes please.

What do you think the difference in intelligence/capabilities would be if there was ever contact?

The inverse bell curve idea sounds mostly right, but it supposes that the more advanced civilization wants to make itself known to the lesser, and I think that's probably almost never the case. Why would aliens bother us humans, at this point in our development? We would just try something dumb and end up hurting ourselves. If there is really some sorta galactic order, then there would be a set of criteria of governing who can hang. I guarantee you that we don't meet that criteria yet.