There is precious little as to what a fighter can do *outside* of combat...
I do think that you and others rightfully harbor a concern about the fighter's ability to influence the OoC narrative with their class abilities, and it's possible that Paizo did not think that it was of core importance. Hopefully there will be further clarification or information about that.
Finally I am convinced. PF2 seems to really not be the game for me. Not that I expected it to be. I am surprised they want to go down this route. I'll rather use 5e or even stick with 3.5/PF1.
They do. This has been confirmed several times. For example, here.I thought everyone got skill feats...