How many fights are too many? I don't know. Depends how "strong" the fights were, and how they were resolved, and if the underlying issue was resolved. If you would come to a compromise and solve the root issue, you wouldn't have those fights. But sometimes people get stressed and you fight about something tiny and insignificant. That's what I call a "stress fight". It happens because someone is stressed out.
So, I try to wait a few hours, or even the next day, before I talk about it. If I was really wrong, I apologize and say how I'm going to fix the issue.
If someone has a specific way of cleaning the house, Dr. Laura says THEY should clean the house themselves, then they have no reason to complain if it's not done right. The other side of the coin is, never complain when your bf/gf does something for you. If they help you clean your house, you have no right to complain about it. Or maybe you're just petty and they should dump your ass. I think this is a great compromise. If you don't like how your SO does it, do it yourself. But don't complain about it.
I have a long time interest in psychology, specializing in relationship dynamics for 30 years.
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