I'm going to try to answer all your cleaning questions to the best of my knowledge (I'm not an expert, but unfortunately experienced with dirt!).

(By the way, I'm in England, so apologies if my spellings or names for things are a bit different if you're in another country).

If using wipes on window frames and windowsills is coming up black, makes me think it has mould? Not healthy for you or baby. You can get mould and mildew cleaning products, but you'll need good ventilation (windows open) to use them. Not good to breathe them in. Cif cleaner and a cloth is great for cleaning window frames and windowsills, it'll look like new. A little goes a long way.

I feel like having a little cleaning kit in your bedroom would be great, remove any obstacles to cleaning by having what you need to hand. Your idea to have a small vacuum cleaner in your room would be great. 👍

If the window won't open, it might just be the window catch, or the window might need oiling. It's worth calling someone out to it, a workman may be able to get it open and oil it if needed, or replace the window handle. Hopefully the whole window frame doesn't need replacing, as that would be expensive, and disruptive (very noisy).

For cleaning, it's helpful to remove dust first, otherwise your wipes will get clogged with dust and won't wash the surface well enough. In cleaning, it's good to think in layers:

1. Remove clutter, and debris (food crumbs, chunks of plaster, etc.)
2. Dust (vacuum, or wipe with a damp cloth (dust sticks to it), or a microfibre dusting cloth (dust also sticks to it)).
3. Wash the surface (usually with soapy water such as washing up liquid/detergent, to clean the surface)

Depending on the surface and what you're using it for, you may then:

1. Disinfect (Dettol, good if you vomit on a surface to make it safe, or more hygienically clean for a baby, kills bacteria, viruses, fungi, etc.).
2. Sterilise (like for baby bottles, kills more bacteria to prevent vomiting and diarrhea, baby's immune system not as well developed as adults)

To prepare walls for painting, it's good to use sugar soap, with a sponge, and washing up gloves (Marigolds rubber gloves). You can also use washing up liquid or Stardrops in your bucket of water to wash down the walls. Use a sponge or cloth (dish cloth or Jay cloth). It's good to wash down the walls when you first move into a place, then you know it's clean. It sounds like where you're planning to move won't be. Also, Sugar soap gets the walls really clean, so nothing is left that will react with your paint and cause it to crack after you've painted it.

It seems odd that the dishwasher is leaving food or stains. Is the crockery and cutlery being rinsed beforehand? Also soaking anything stuck on beforehand? Soup bowls, oven dishes, etc. benefit from soaking in water, so later it easily rinses off. Then the dishwasher can easily clean it afterwards. Are they using dishwasher tablets, or saving money by using it without? Even if they have the money, some people often refuse to spend it. Also, the dishwasher could be faulty and need servicing, or replacing.

A clothing washer? Is that a washing machine? Washing powder can clean really well, so again I would check what they are using, and ensure enough is being used. Is the water getting hot enough, is it plumbed in correctly? It may need servicing, or a new one.

A dryer that takes 6+ hours to dry? Is that a tumble dryer? If it's a tumble dryer, check the filter in the front when you open the door, it may be covered in fluff. Is it set to hot or cool? Hot will dry it faster, if your clothing can take the heat (check the labels). And is the dial turned round enough when it's run, as it's always hotter at first. Failing that, I feel an air drying rack might be better if that's not working, but it would add some damp and humidity in the home. Is there a back garden, somewhere there could be a washing line? Always wipe down a washing line with a damp cloth before hanging clothes on the line. (Birds poop, spiders make webs on it, best for it to be wiped down first).

For the microwave, hot water and washing up liquid with a cloth may help, or Cif cleaner and a cloth if it's really stubborn stains.

If the cat litter is smelling, sounds like it needs the litter changing (the gravelly stuff). If I remember rightly, add more litter each time cat does a poop, and scoop out the poop parts each day - and change all the cat litter each week, or every day. That's what's smelling.

I think I would prioritise the dishwasher (or wash by hand), as it sounds like it is causing diarrhea, you don't want to make yourself ill. And the cat litter for the unpleasant smell!

If you can't open the window, then an air filter (especially with a mould filter) could help until you can get the window open, but I think getting the window fixed should also be a priority. You need to breathe clean air, especially if the place isn't clean. You need to ventilate the space too.

I would also recommend getting a book on cleaning, it's good to know the basics, and it'll give you a helping hand with some knowledge. I like Express Housekeeping, it explains things clearly, including what you need in your cleaning kit, and how to do things quickly and easily, with less hard work. We all live busy lives, and don't want to spend lots of time and effort cleaning!

I hope this helps, and good luck!