#1
Does anyone have an idea of the biggest gauge i could use without having to file the nut? Does filing the nut stop me from using lighter string gauges afterward?

I just put on 11's today and I may go up again.
#2
Without touching the nut I'd be surprised if you could go above 12's but whenever you change gauge it's going to need a full setup anyway so sorting the nut out shouldn't be that much of an issue?
#3
Long as you adjust the neck, etc properly, you could get away with pretty much any gauge. Friend of mine uses 16-70 or so - in drop B but still.

Do be aware that at some point, standard tuning won't be an option anymore because of the required tension on the string causing it to snap. Not sure what point that'd be on a Strat, though.
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#4
I think it depends on the individual guitar. I have a fender strat that came with very small nut slots that needed to be widened to take 11 gauge strings properly. 12s might be fine on your strat - it's the kind of thing where you won't be able to find out until you try it.
Rig Winter 2017:

Fender Jazzmaster/Yamaha SG1000
Boss TU-3, DS-2, CS-3, EHX small stone, Danelectro delay
Laney VC30-112 with G12H30 speaker, or Session Rockette 30 for smaller gigs
Elixir Nanoweb 11-49 strings, Dunlop Jazz III XL picks
Shure SM57 mic in front of the amp
#6
SRV used 13s and sometimes even thicker. You'll have to set it up for heavier strings (relief, nut, trem), but the guitar is probably more capable of handling fat strings than your fingers.