So the upside down. Is that solely an alternate version of our own dimension?

That's what it appears to be, yes.

Were there already living things in the upside down before El opened the first gate? In one scene we see her make first contact with the monster, it already appears to be feeding on something, perhaps from a different dimension entirely?

It's implied that there are other creatures in the Upside Down. In the finale we see the egg that Hopper takes a moment to look at. The only other creature besides the Demogorgon that we see is the slug that Will barfs up.

The scenes where its totally blacked out is not the upside down no? Its just her kind of searching/contacting space?

The Duffers refer to it officially as "the void", so it's more of a mental space that El is able to tap into with her powers.

How did no one else in the town bleed enough to be taken? I guess maybe animals were fed on, it opened the gate in the woods for that deer right?

There's a lot of debate about this, but ultimately I think the rules aren't meant to be too strict on when and where the Demogorgon is drawn to blood. It seemed to only want to come to areas close by to the lab where the main gate was, so my assumption was always that it's too afraid to travel too far so it goes to the closest blood it can sense.

Bonus S2 question. Am I the only one who instantly distrusts the new girl joining the group? Something instinctively tells me she's bad news man.

Nah I don't think so. Billy is her step brother and he's the one who's meant to be an antagonist.