1) MOA with 1/8th minute turrets is the most common by far. The finer adjustment comes in handy for F-Class, where 1/4 minute or 1/10th mil "clicks" can be enough to put you out of the 10-ring on the other side.
2) 2nd focal plane; typically, FFP reticles are thicker relative to the target when set in the upper mag ranges. This tends to obscure more of the target than you really want for F-Class. Further, no ranging is required for F-Class, so FFP is not needed.
3) I have several NF scopes on F-T/R rifles; 8-32x56s with the NP-R1 reticle, and 12-42x56s with the NP-2DD reticle. Both reticles have their pros/cons. The NP-2DD is basically a dot reticule, which I really like for LR (>600 yd). It is easy to use and very open (uncluttered). However, estimating holds with it is more challenging than with a typical hashmark reticle. The NP-R1 is also a great reticle; it has hashmarks and so is a little more cluttered in the center than the NP-2DD, but can be used more easily to estimate holds. A lot will depend on the type reticle you prefer. Whether you like dot or hashmark, simpler and less cluttered is generally better for F-Class.
4) I would recommend upper mag of 32X-42X range; 22X is not enough. You can go higher than 42X, but mirage can quickly become an issue, and the risk crossfiring goes up dramatically with the smaller field of view. I usually run mine between about 30X and 42X depending on mirage conditions (NF 12-42x56).
Edited to add: You may need to think about overall scope weight if your rig will be close to the limit; also, total elevation adjustment may need to be taken into consideration. The 45 MOA total elevation adjustment on the NF 12-42x56 wouldn't be enough for my .308s without a 20 MOA base. The newer "Competition" models have 60 MOA. Just be aware, for a .308 you'll probably need somewhere from ~28 MOA to as much as 35 MOA to get to 1000 yd, depending on your load, barrel length, etc. Other calibers will obviously vary from that but just be sure whatever you go with has enough adjustment. Rule of thumb is that you'll get slightly less than half the total elevation adjustment advertised for the scope, plus whatever extra your base may provide.