What can I do to shorten things up a bit? Are there any mods anyone recommends that will not change the gameplay totally, but speed things along just a little?
It's OK, the first couple of games are long as it takes a while to get used to it.. once you get more exp, you'll be bashing small maps wi one AI in under 30 min.. 
I've noticed in a lot of pictures for these mods, a lot of players have a very very shortened UI, giving them a much larger empire tree, and broader view of the galaxy and what's going on with all the ships. How can I set this UI? I've tried looking in the UI settings and I didn't see anything for it. Is it a mod? Is there a file I have to edit?
I think this is relatred to your video resolution.. Try setting a higher res and the UI will adjust accordingly..
Is playing in the single player missions even worth the fun? I have to say that I'm a bit astonished with how fast the AI builds up, even when it's just set to normal. I have a very hard time keeping up with it, and not getting my butt kicked. Are there any good Multiplayer communities playing this game? I don't want to join one and end up having my butt kicked by human players as well.. =/ I know that's a part of gaming, but still I want a chance to learn this.
Well, personally, if you can't beat the AI, don't bother trying to beat human players
The AI build up is actually quite OK, unless you set the AI to Hard or Unfair. I do agree that in the beginning, it appears as if the AI seems to build up really fast but the truth is that experienced human players build up even faster. One suggestion is 1. set the AI to be the same race as yourself, then 2. look at the replay and see what the AI did in their build up on their home planet. That should up your learning fairly quickly.
How can I speed up my resource intake. Even on that 7 planet system I was mentioning before, I owned 3 of the planets, and the AI owned 3. It seemed like it was taking FOREVER to pull in both metal and crystal. And my credits were never able to reach above 4k, without me spending it on ship production, planet production, or research. I've only really played the TEC and played the Advent once, but since I'm still fairly new to the game, if anyone has any pointers on how resources can be pulled in faster, I'd greatly appreciate it.
Well, I think you're actually on the right track. If you have three planets, make sure that you have upgraded the planets to max. Secondly, add in civilian research to bump up your metals and crystals production. Perhaps you are a little "anxious" is all
Don't worry too much about not having more cash above 4k. If you save all your cash in early/mid game, it probably means that you are not spending it on something you probably need. In TEC, the resources/economy generation are actually what the race is famous for, so just keep going. Probably, the only item for discussion or debate is the choices you make in research and ship production. For that, do check the Strategy section of this forum for more tips on the different approaches.
Overall, I think you're doing just fine.. Have a bit of patience and faith in yourself and I'll bet you'll be a pretty good player before you know it 