Is my place considered inhabitable?

I just moved into my unit in a condo on Saturday. The place was not cleaned so I cleaned on Saturday and called around about getting professional cleaners in since I needed the help. Cleaners made the place a lot better with a deep clean, which consisted of grime in the bathroom (tiles, floors, and walls), insect droppings in the light fixtures, insect droppings in cabinets, fridge, oven, vacuuming, mopping, etc.

This afternoon I emailed and texted my landlord about the issues below and getting reimbursed for the deep cleaning, currently awaiting a response. In addition, I contacted my rental agent and they said to contact the landlord as they don't manage the property.

• AC unit #1 – 1 filter is stuck and I was unable to clean it, the one I was able to change was dusty. Noting this because the lease states that the tenant is responsible for changing the filter.
• AC unit #2 – has dead flies and rocks inside so I turned it off.
• Tested the fire/smoke alarms and none were operational, one was not even posted and tucked in a cabinet.
• The kitchen faucet potentially has mold, I tried soaking it overnight in vinegar and cleaning it with a brush to no avail.
• The toilet seat was stained yellow and peeling, I'm hoping to replace the seat myself.
• Water damage in a few areas with paint peeling and crumbling.

I looked up my lease agreement and what uninhabitable is defined but it seems vague. However, I don't think these issues would make the place "uninhabitable." The AC and kitchen faucets are my biggest concerns, hopefully, both will be repaired or replaced. Any advice on the next steps to take besides waiting on the landlord for remedies? I've put in quite a bit of effort to make the unit livable but I think I'll wait to see how the landlord responds before further investing more time into cleaning. I documented the conditions at move-in and have the photos saved down. Based on these issues, is there cause to consider the unit uninhabitable? FYI I have renter's insurance and the rental agent told me verbally that at the showing the landlord would clean the place.