I think this week will end really badly for Manchester City. Because I believe Liverpool, Arsenal and Aston Villa all are in a situation to be able to win their games this week. Liverpool can win against Manchester United home easily while Manchester United are bad at defending. Arsenal should be able to beat Brighton home as well.
Aston Villa are playing an away game against Brentford but Brentford are really bad this season. They were able to win only once on their last 5 game weeks in the league. I don't think they can hold off Aston Villa from winning another game.
I think your Manchester City prediction this week is too optimistic. Liverpool, Arsenal, and Aston Villa have been playing well, but football is unpredictable. Take Man City's recent home game performances, for example. Despite their Champions League success, they've remained unstable. However, dismissing them may be premature. Inconsistency doesn't necessarily mean tragedy.
I don't think Liverpool will easily beat Man United. Although inferior, United's defense isn't always bad. They may surprise. Arsenal should beat Brighton, but football's unpredictability is its charm.
Despite their terrible form, Brentford could push Aston Villa. Football isn't always easy. Your predictions could be right, but I wouldn't bet.
In the next game between Arsenal and Brighton, I think Arsenal should do anything they can to beat Brighton and win the game to get the full three points in this match because currently there is a close race in the top side of the premier league as always, and in Liverpool is in the first place with only one point more than Arsenal with means if Arsenal wants so try their luck to back in the first place of the premier league they should beat Brighton and hope to see Liverpool losing some points in the next game.