Can you let players travel to other planets and have them build cites and have battles there?

I hope that you will be able to do tht. There isn't any 'definite feedback given from developers. It may be possible though. However, each planet has a reason for it to be obtain and placed into the world. Most the galaxies in eve do have vacantcy... Planets that have resource but are not owned... Its all relative to how close everything is... For example, if you are out of the way or far off into the galaxy you will have to bring stuff to that planet yourself.

I'm not sure how much that will carry over with the Dust514. I sometimes think you will just be a hireable guard or attacker... However the way the devs have explained it.. In numerous presentations... You will be able to have your own corporation; your own planets. I'm not sure if you control the layout of that planet, or if it is all just automated sandboxed layouts.

In eve there is also pirates... I really hope they pan that out into Dust514 or at least give that ability to play lonewolf mercenary or lone squad mercenary... That would be awesome.

There is also a campaign aspect inside the game that breaches into the game world.

I've heard a few community staffers say, it may not have many different maps -- I'm not sure how accurate their info is from time to time, because I've seen videos of developers saying that you will have a massive load of options... Not of just character customizations but also corporation creation that would seed into the eve universe and its politics.