I agree with a lot of your points especially the ones that have to do with the team spirit and togetherness. Don't know the "one of our more experienced players" you're referring to but if it's the one I think you're referring to, I'd say the guy has a very good relationship with other players. You can tell the way they respect him and acknowledge him. You can even tell from the way he celebrates with the rest of the team from the bench when we score an important goal jumping on players and acting like a 5 year old. I also think the players see him as quite funny and he revels in his hilarity.
Re: Sanchez, if we don't get him, then fair enough. We'd look for someone else but I've got to be honest there are so many boxes he ticks. Any opportunity to continue to advance ahead of our rivals should be taken seriously.
In terms of ability alone, I don't think our players are so far ahead of the competition. My EPL teamXI front 3 would have Sanchez, Hazard, Salah, Kane, Mane, Eriksen in contention and I honestly don't see Aguero, Sterling and Sane as first choice out of that lot. This is my view with respect to defence too however in midfield we are head and shoulders above the competition.
The difference has been Pep, our goal keeper, full backs and the spirit of togetherness that you mentioned. My fingers are crossed to see how this all plays out.