Point 1 - How do you know he hasn't identified players? Do you have access to his emails?
Point 2 - Again, how do you know what his performance agreement is, and in terms of the building of the squad, I addressed this in my original point. He has clearly identified and signed a number of younger, potential players, and the manager refused to play them. Is it the director of footballs job to pick the team and tactics? If so, that is not what I would consider to be the "traditional" role, as you suggest.
Point 3 - Surely, a working relationship between a Manager and DoF is a positive, and not the negative you hint towards by stating that it was in fact some form of nepotism that got Allardyce the job, and not his track record and our complete and overwhelming panic as we floundered to the foot of the table.
In my mind, his role is to oversee, he has identified players, he has ensured, in his role, that the players identified by the manager and his scouting team have been signed. Other than Giroud and possibly Van Dijk (if rumours are to be believed), I can't think of another player we actively tried to sign and didnt.
I wouldn't say my reply was any weirder than yours, and you didn't really, and still haven't, actually answered my questions.
Take care. Hugs.