I wouldn't describe spending £17m on Claudio Bravo as cheap personally, I'd say that's a big fee for a keeper. As for Donnarumma, do you really think he will be leaving Milan in a hurry? If he continues with his current rate of progress he'll only leave for Real or Barca, not Arsenal! You've been playing too much football manager if you think he's a realistic target for them.
Do you honestly think Arsenal only sign young players for profit and not to play in the first team? Ramsey, Walcott and Oxlade-Chamberlain are proof they don't, you can also add players like Wilshere and Iwobi who have come from the academy.
If a player is good enough, they will get a chance at Arsenal, but it's difficult to break into Champions League side, so less players do it, but it's not impossible. If a player is good enough he will make it at a top club, just ask Kyle Walker.