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'm not sure Manchester City will suffer this week. Arsenal and Aston Villa are likely to win, but Liverpool's match with Manchester United is less likely. United can surprise in big matches, especially ones with historical rivalries like Liverpool, despite their poor defense. They might draw, which isnt ideal but better than losing. United's underperformance may motivate them to perform in such an important encounter.
Arsenal looks good against Brighton in the second game, and Brentford may not challenge Aston Villa. Football is unpredictable, and under pressure, teams can perform well. Although Arsenal and Aston Villa are likely to win, I wouldnt stake everything. When least expected, underdogs can win.