When I get to mars, what can I expect? Does it automatically create another island/claim over there for you, can I tp back and forth from mars to the moon and back? If I want to live there should I take all my stuff that's in my moon base e.g. chests, observatory building blocks? Is it like the overworld/moon but a mars version?
You can not expect anything. You will not get a claim on mars, I would also not recommend to life there, because theres no protection (=no claims) and MobGriefing is true. You can teleport to you moon base allways by doing /is home. To teleport back to Mars use the Matter Transmitter + Receiver from RFTools Mod. Mars is kinda like a red moon version, but you will need thermal clothing to survive on it. I hope this has answered all your questions, if not do not hesistate to ask further.