Couple minor things I would like to point out, first being thermal clips were introduced after the geth attack on the Citadel, somewhwere before ME2, so your weapons have heat sinks. The next is we're focusing on a character driven store and kind of moving away from the video game structure. As such, having levels on equipment is unnecessary, so the base weapon is fine and we tend to like people not to shoehorn themselves into the game's classes. You can pick skills from any of the soldier skills, not just the one class. You can also pick more than three.

Another thing is the game's about mercs scraping by in the galaxy, so chances are, your character wouldn't likely have access to expensive military hardware, since that's A) issued kit he wouldn't have for personal use, especially after being discharged, and B) he's going to have to buy most of hus junk out of pocket, especially things like rocket boots. Things like the Warfighter amp, aren't necessary. 

Onto the history!

One thing I need to point out is turian military personnel are all conscripted, so your character would have had to serve regardless of political atmosphere, and if anything, the turians would want to be keeping on edge over humanity showing up on the galactic stage. Picking the 26th as his career goal is totally good, but he likely would have been given his posting after graduating from basic military training.

For the most part I actually really enjoy the character and his history (I laughed out loud at the Fornax bit), and honestly think he'll be a great fit! Couple more things you need to address, though:

First, if it's military issue and it's not footwear, head dress, or gitch, you don't get to take it home, period. That especially applies to very expensive hardware and weapon tech, which is a biiig no no. As well, he wouldn't be permitted to modify military kit unless he was authorized by his unit and was an armourer. It's government property, and modifying shit while remaining untrained and unauthorized is a great way to get court martialled. Plus, he's a soldier, not a tech expert. He shouldn't know how to do that stuff.

Next, Nova hardly has a reputation and has barely had more than a high profile missions which are small scale compared to more established and better funded groups. You may wish to work on why and how he came into contact with the team. Also, he's not beginning the RP as a member of Nova, he's going to be recruited in a way we all have to discuss to see what works. It's kind of strange to have an established game that's been running since spring last year and suddenly pretend there's this one character that nobody acknowledged or spoke of or to before just there out of nowhere.

Lastly, because of that, he's not going to have a room because they're all claimed. Something everyone needs to talk over.

Overall, a great start with some pretty simple fixes! :)