Hellboy/BPRD and Aliens/Predator and the different Star Wars lines are the only things I can think of that cross. Is there an actual finite "Dark Horse Universe"?

Short answer: No. Long answer: Not really. Dark Horse is rather like Image, in that whenever there is a crossover between titles, it's generally more a one-off thing, although I believe they did have a stab at a "DHU" in the 90's (don't quote me on that). Also, BPRD is more a spin-off of Hellboy than anything else, albeit a very well-written one.

Richard is right in a sense. Dark Horse lines are mostly self-contained. But Hellboy and BPRD are in the same universe, self-contained in their own line.

Dark Horse comics had a Universe that was titled 'Comics' Greatest World' in the 1990s and it appears to still technically exist, it's just rarely used. Such characters who were featured in this sort of multi-title universe included such characters as Ghost, X, Monster, Titan, and more. To be honest, the characters were pretty well written, unlike the obnoxious creations that got Image off the ground such as Supreme, Troll, Youngblood, etc. I actually discovered this after I decided to do some research on an issue I'd found called 'Comics' Greatest World: Monster' which was part of a 12 issue series, each one debuting a different character that would go on to make up such a world. The three most popular characters had to be Titan, X and Ghost [Whom had a crossover with Hellboy and even Batgirl!].
 
It's likely that this project flopped as Image was at the time starting to establish itself under Liefelds EXTREME era of comics.

It would be wonderful if Dark Horse Comics continued to produce comics featuring their own characters.

I wonder if they don't do that because they feel it would not make enough money or if it would interfere with creator owned comics and licenses for Star Wars and others.

Ironic, isn't it Dark Horse? It was low sales that drove Comic's Greatest World off and now it's low sales that'll give us the chance to enjoy Dark Horse Heroes once again... One little advice though from a customer since 1991. The current Ghost series is, any way you look at it, a flop. The first story arc's quality was mediocre at best. If you keep letting this happen, the next thing that'll be driven off is the company itself. It's the perfect time to bring in a new creative team.

Is Captain Midnight owned by Dark Horse Comics?

Or is Captain Midnight only licensed by Dark Horse Comics?