Assumeing you live through it can you take the new wepons you've erned back into the Mojave?
Correct. Every pound of stuff in your inventory when you return to the Mojave is yours to keep. There's also a vending machine in the bunker, so you can use your SM chips (and turn in clothes and cigarettes for more.)
You'll also get all the gear taken from you when you went to the Sierra Madre once you go to leave the bunker.
I assume you return there after this side mission.
You return to the Mojave, yeah. However, once you've left the villa and returned to the Mojave, there is no way to get back to the Sierra Madre.