There are not any I've heard of that support all the items you're looking for off-the-shelf.
I haven't played EVE, but friends have, and I seem to recall it being limited jump points.
If, however, you drop the space hazard effects, there are several.
GURPS is capable of it... but you'll be looking for multiple books. And GURPS 4E is only a slight bit different from 3E. Vorkosigan Saga RPG (Powered by GURPS 4E - 4E Lite integral) has a good baseline for what you're looking for in terms of rules, but you'll need to augment it with some other supplements. For good trade rules, you'll need GURPS Traveller Far Trader. (If you can wrap your brain around the math, and can accept the lack of effect of the comm lag... but given the different setting, it may be less an issue.)
Traveller in it's latest incarnation (Mongoose Traveller) has most of what you'll need in the core, but you'll need the Psionics book (for the mental imaging and transfer rules), and the High Guard book (for the expansions to ship design - you may want to keep tonnages down, tho', as the Bk2). Further, the core trade rules are excellent.
If you don't mind a little bit more work, R Talsorian Games' Mekton Zeta has exquisite combat and design rules, albeit a bit vague in labeling. It also mentions brain-in-box. What it doesn't cover is the actual brain-taping and cloning, nor trade.
Hero System can do it, but it's a matter of knowing how to work it in Hero System terms. You'll need Star Hero (and if it's not the late 80's edition, the corresponding core rules; the late 80's edition was a standalone). Again, you'll need a trade system. Plus it's a
d6 Space can easily cover everything but the trade rules and brainreading, and the starships book expands the ships nicely. You may want to find WEG's Star Wars Galaxy Guide: Traders if going that route, tho'.