Should I request repairs if I’m not following everything in the rental agreement?

I don't have much experience renting and I've never put in a maintenance request for anything before but I would like to do one regarding the insulation for the house as well as some other things.

However currently we are breaking the rental agreement in various ways including having more animals than we should, blinds and some walls being torn to s**t because of said animals, fire alarms not in place, etc. I plan to fix all of this before moving out but it's a slow process and I'm worried about getting evicted if I put in a maintenance request.

Am I right to play it safe or is there something I'm not seeing?