1.)But I did want to win by military, but there was one planet I couldn't take. My transports would do nothing as I moved them in. Then I noticed there were some ships in orbit, but when I tried to destroy them with my attack ships, nothing
As long as your ships have some attack they will engauge. GO to interface options and enable full battles and you can see exactly how your ships are fairing and why.
2.) Do new techs (like weapons and drives) apply to all ships or only new ones built?
No you need to design a new ship. But if you upgrade an existing ship then all planets producing that older ship will switch their building to the newer model, even if half way through.
3.) I built a few Starbases, but I didn't see the purpose. What exactly can I have military bases do? Do mining bases automatically give me their benefits, or do I need to do something?
All give benefits automatically depending on what you have installed on them. For mining just let the space miner do its thing and forget about it.
Other types of starbase will only extend your ships range if built alone. You must send extra constructors to add modules, and these you can see what benifit they provide as you select them from a list.
4.) I really wanted to make an allience with one of the computers. I researched the alliance tech and then traded it to him, so that we both had it. Our relations were very friendly, but I never saw an option to ally. I assumed it would be under the "Speak to" window with the trades and stuff. How do I make alliances?
5.) Does anyone have a image (.jpeg or other) of the complete tech tree, that could be printed out on a plotter printer or something?
You can toggle on the full view.
Alot of this is covered in the tutorial, you might want to watch those in full. They are actually quite helpful.