Mouse+ Keyboard work and also Xbox 360 controllers. No Keyboard only because the mouse is used for aiming.
I have not actually found any one else's body yet so I am not sure how that goes, I have only read that it happens.
As for the length of the levels, they can be quite long if you want them to be, or you can exit and go to another level about half way through (you will need a "sector pass" to exit, and those always spawn after you have collected a certain amount of cargo in your current level). There is incentive to replay the same level again and again, however, because you can get higher scores for the online leader board. You can also return to any levels you have already been to without using a sector pass. Sector passes are only for creating a new level (using a new name for the random generation). In my experience, I end up dying before I actually get to the end of a level but i can get 20-25 minutes in before that happens. I don't know the point at which levels end but they are long if you want them to be.
All upgrades to your character are self-contained within the level you are playing, but you get upgrades to your ship that are persistent. For example, after achieving the first rank achievement you get the upgrade station itself, second rank gets you 10 free points to spend on upgrades at at the beginning of every level (you normally have to collect these points inside the level), and third rank gets you a maintenance station with a few other useful functions. I have read that fifth rank unlocks a new mode that allows you to turn the wormhole timer off so that you can just explore the random worlds without fear of being sucked into space every few minutes.
In case you can't tell, I am loving the game so far. Here is a new write up from QT3: http://www.quartertothree.com/fp/2012/10/16/what-a-difference-a-font-makes-in-cargo-commander/