1: Sell shit you don't need. You only need 1 weapon for the fight (and the run up leading to it). What weapons do you have and how are they upgraded?
2: Run, don't gun. The black dog things with 3 tentacles are the biggest problem damage wise, and the biggest ammo-eaters (at least for the plasma cutter).
3: You don't need stasis packs - just patience. With full stasis duration, you can stasis Nicole, run up, melee, wait for the recover animation, and melee again. If I remember correctly, you can hit her again once she raises her arm up. I don't know what difficulty you're playing at, but this took about a dozen "stasis, melee, melee" rounds while on the level 3 difficulty setting (zealot? the one before hardcore). You don't need stasis packs at all, just patience. Obviously stasis upgrades (duration, capacity, recharge) help, as does the suit that decreases recharge time. And remember to let the stasis recharge after every time you do a run on her - otherwise when she dies and you get mobbed, you'll be stuck at 0 stasis charges left waiting for a recharge.
4: Yeah, the stuff they drop is random. And you have to smash shit to get the items out. Stasis, melee, melee on a group of them should give you plenty of items though. Again, if you're carrying a bunch of different items you're more likely to get a bunch of different ammo types, making reloading and weapon switching an issue. I don't know if holding many weapons also decreases your chance of getting health packs, but it might.