'Top quality' and 'World class player'. Easy to state, but his performances at Arsenal do not suggest that he would improve our squad in anything but numbers and reputation. He is 12th in league goal-scoring charts and 42nd in the assists charts. I think you are mistaken if you think it's down to attitude. I watched the Arsenal v Chelsea game last night and he ran himself into the ground, so much so that he scarcely touched the ball in the 2nd half. He had a good 1st half, and a poor 2nd.
He was world class by any definition. But players can slide quickly. And he is. Thankfully we have less than 4 weeks to see what Pep will do. Setting aside the pros and cons, the fact that we do not have an agreement in place with Arsenal suggests to me he is not going anywhere this window. Southampton did not want to sell VVD in the Summer, but Liverpool obviously worked at it over the Summer, and the deal was in place. If we had a serious intention to bring him here, I think a deal would be done, and Arsenal would have had a deal in place. Obviously still plenty of time for things to change, but the fact that this is an old target suggests to me that some people are barking up the wrong tree.
That's a loaded question. Clearly if he would significantly strengthen the squad we would try and do it. The more basic questions are would he significantly strengthen the squad, and will Arsenal sell? Both are matters of opinion. Arsenal had no intention of selling in the Summer, because they did nothing about it until the last day and once again there's no sign of an incoming Arsenal player to replace him. If you see Arsenal agreeing a deal with Mahrez or Lemar etc, then I'd say that they are preparing to sell him.
We're 20 odd points above Arsenal. Logically, at the age of 29, he should be having an absolutely amazing season for us to consider him. He isn't, therefore the enthusiasm to sign him seems misplaced to me. At bayern, Pep signed Alonso. He was an old player, but an old player in his prime whose game, passing, was not going to be affected significantly by age (Gaz Baz). The argument for signing him is restricted to a short term possibility that we may never have an opportunity to win a domestic treble again and Sanchez may help us to do that. An extra pair of legs would help now, but even so I don't think he is enough of a match-winner or an outstanding player that justifies 3 years in our squad at the expense of alternatives in our youth team, and unidentified players in the future. For me players like Maitland-Niles, Ozil, Wilshere are more important for Arsenal. He's not even the best player at Arsenal any more and yet some City fans are convinced he's a vital piece of our jigsaw?