For the love of all that is pure and clean may god have mercy on your poor soul...

I'm in no way an adult doing adult things, but I have a pretty severe dust allergy which means I have to take cleaning into my own hands a lot of the time. The one thing I recommend doing is dusting as often as you can stand it. Seriously, dust just fucks every little thing up and I'm pretty sure if you looked up enough studies you would be petrified by what is in the air you breathe when its really dusty.

Second most chores have to be done in accordance with the mess being made. For example if you aren't using too many dishes you wouldn't be washing the dishes as much. In your case it seems like you are one force against an even greater force that is your roommates. Although those numbers you researched seem high or excessive in your case they may not be. Cleaning always works in accordance with how much of a mess is being made. Currently I dust around the house 3-4 times a week and I vacuum my floor twice a week. My family luckily divides chores up so it isnt on me. The other issue like I mentioned before is doing anything four times a week seems excessive unless you aren't the only one. If you got one other person to help now you only have to do it two times a week.

Third part: You've got to set aside time everyday to do it. In the same way you plan to clean the house, clean your schedule. Get organized to clean, and be prepared not to finish it all at first in your case. As you clean and begin reaching a reasonable level of cleanliness the job gets easier.

Fourth, get someone to check out that drain. Seriously, get someone to check that drain out. Get them to snake the drain and then tell you what exactly is wrong and how to fix it. I don't have much experience in that field, so that's the best I got.

Fifth, CLEAN THAT RIGHT NOW!!!! That is a huge fire hazard. Friend of mine set his town house ablaze because he didn't clean that shit for a really long time. Obviously it may possibly never start a fire, but it increases the chance greatly.

Finally, I have a few tips I could give I'm just at work typing this out because yes I could be working, but this seemed far more urgent.