Froob agents are teh win !
For weapon either go cater+scope or X-3 with TIM scope (or whatever that doesn't debuff your inits). Cater is probably nice for doing easy solo missions, since you'll be able to AS almost every mob. Prefer X-3 for teaming since you might want to just skip on AS depending on the situation (no decent healer, hard team missions, ....)
As for other armor, what should I be using?
What people said above. And consider virral eggs for shoulders if you can afford some (+30 int/psy +300 hp/nano and +6 damage for a pair)
Also, is it at all viable to do any FP at this level?
Always start your solo session by FP:MP and cast heal/attack pet (more damage can't hurt). Then either pewpew for 30 mins or /terminate (to cancel FP, you'll keep pets for 2 hours - or till healpet is out of nano) and then either stay in agent if you want to use root/snares or choose another FP for buffs (I liked soldier for reflect shields/total focus and fixer for runbuffs and grid ability). I also had most top shop buffs uploaded (reflect, runbuff, essence, doc team HP, ...) for teams (when there is a real doc making my healpet look like some utter crap)
Mimic:Enfo started being worth it at early TL5 (rage for runspeed and those annoying rooters/... mobs, mongo - and healpet if you can FP:MP & /terminate - to stay alive and challenger for extra damage, and of course the essence/shield/init buffs).
By changing some implants, I might be able to make a decent use of Mimic:doc now at 160+ (but certainly not self casting best heals for a while)
Mimic:trader seems great for damage, but I never liked trader playstyle, so didn't really use it yet. It's also the only mimic that will let you rebuff UA/TTS/... while mimic is still running (don't forget to refresh them before recasting mimic !)
Mimic:sold seems more a PvP thing and the other ones don't have any real use in mimic.
And with last patch, give a try to daily missions. Every one should be a guaranted ding and you might be able to visit an alien ship as a froob
(if you get that mission, I'd recommend doing it the "agent way") And most of them are quick enough to complete to fit your casual playtime.
P.S : if you use the /terminate trick, make sure you saved all your XP before. Dying this make makes non-saved XP disappear instead of going into pool. And also it might not be worth it for a while : you'll keep pets but not all buffs (and you will need MP buffs to cast UA/TTS)