^
Gabriel Jesus is surely more affordable for Arsenal. Besides as you also said Arsenal don't have a very serious chance to sign Sterling if Chelsea are very decisive about finishing this deal. Chelsea have a big advantage of joining the Champions League group stage directly while Arsenal aren't in the same situation. Arsenal's missing the Champions League by inches caused them to have a worrying transfer window. As long as the player himself doesn't dream of playing especially for them they won't have a bigger chance.
^ Yes exactly, Only if the player really wants to play for Arsenal and it is going to mean a lot for him to play for Arsenal and if the player is not worried about playing in the Europa League instead of playing in the Champions League, Arsenal has a chance of getting that player.
Otherwise, it is really hard for Arsenal, I think that is why even though Arsenal has been linked with a lot of players they have not been able to confirm anything.
Manchester United has been slow to take advantage of the transfer market this season. Indeed, there are still many internal matters where Erik ten Hag will find it increasingly difficult to fix the formations. On the other hand, Liverpool and Manchester City are so quick to take advantage of this situation so that they are increasingly in front to lead the English League next season. Support for Erik ten Hag is still so lacking that it looks like a lot of work has to be postponed. De Jong also never finished signing his contract.
Slow only this season? They have been slow in transfer window for quite some seasons now. They dragged so much time getting Sancho so yeah they do take quite a time. The thing is that they always bid below than expected and when the club gives them a bid to match to let the player leave they always try to propose them a bid lower to that + add ons. So in short, their proposal always falls short of what the club expects them to match. It's the same story going on with De Jong right now.
^ You can expect this type of offer from Manchester United because they have wasted a lot of money previously bringing in overrated players.
So now they have to maintain some big caution trying to bid for players. They cannot just go crazy and place any amount of money for a player. And for that reason, they are losing to a lot of other clubs and not getting the players that they want. De Jong can be great for Manchester United but I really don't know if the same thing is going to happen.