Yes this season will be a tough test for Arteta to be able to deliver something that Arsenal fans have long coveted namely the Trophy, but it is not easy for Arteta to make that happen when they have to compete with Liverpool and Manchester City, what you say is true because after all this is a crucial time for Arteta and he must be able to bring out all the skills to be able to give his best for Arsenal, so far the pupil have beaten the teacher in their first game of the season, and it is important for pupil (arteta) to beat teacher (Pep Guardiola) again in the second meeting this weekend to keep Arsenal's chances of winning the trophy this season alive.
Honestly for the Liverpool and Brighton matches, I personally might see Brighton will be able to surprise Liverpool in the match later, indeed so far the draw between Manchester City and Arsenal is what Liverpool expect, but they should be more focused on winning the game against Brighton which has often given nightmares to Liverpool no matter it is home or away and my prediction Liverpool and Brighton may also have the potential to draw the game later.
Arteta went through a situation like this last season and they failed, but what has passed can be used as a valuable lesson so that it doesn't happen again this season.
Competing with Manchester City and Liverpool is not an easy thing because these two teams have a much better mentality than Arsenal, but they should not be favored. Arsenal could be a turning point for them to prove it.
The match against Manchester City will be everything for Arsenal for their mentality and self-confidence. I am sure that if Arsenal succeeds in winning this match, the confidence of the Arenal players will increase drastically.
I don't think Brighton will be able to hold back Liverpool's progress, surprises are possible but we also have to look realistically if Liverpool's performance is much better and they have much greater motivation because the Liverpool team is competing fiercely in the race for the title this season.