Pedal strike - ride bulletproof pedals and cranks you don't mind scratching. Those strike usually don't hurt you and if those parts are robust, they survive also.
I haven't done tons of off-road on fix gears. I have ridden Cycle Oregon a bunch of times fixed and in recent years they've had gravel stretches. On decent roads, fix gears work really well. I find I am comfortable on skinnier tires fixed because of the feedback from the rear wheel and our automatic reflex to back off as it starts to go to one side (like skilled drivers with standard transmissions on snow). Now, downhills are a challenge. Brakes help a lot. So does changing to a higher gear/smaller cog. I did the roughly 1700' of descending down the Trask River logging road in western Oregon on a 42-12 on 35/38 tires and really good cantilever brakes. It was an ear-to-ear grin blast!
Get good on the fix gear on pavement before you go off road. Riding fixed, the drive train is in charge, not you. That has to be second nature. (And the caution - you might just find riding fix gear is addictive. I got hooked my first ride 45 years ago.)