I tried to do some mining. It worked with parsteel, but when I click on an empty tritanium field I only get a grey circle that turns (wait while loading the information) but it never shows any info. When I click on a field that's occupied by another player it immediately show the data about the player. Am I doing something wrong or is there another way to mine a field?

Mining in this "game" is broke AF. A lot of the tritanium mining spots are bugged for everyone, not just you. That's why there's no ships on the free ones.

I'm in an alliance and there are buttons to help other members. What exactly does that mean, how am I helping them if I chose to click on the button? Does it transfer some resources of mine or does it send them speed ups?

I am hoping I am right here, it sends speed-ups. I've got like a hundred 1-minute speed ups, but when your builds need 12+ hours, a minute ain't worth much.

One last and possible stupid question: How do you change the name of your ship? It always says Ship A or Ship B. Other players have names next to their ships.

You can't. Neither can anyone else. The name that shows is their username.