OK, practical things.
Can you put up a push to fit shower curtain pole and put in a shower curtain? Reduces water splashing, no physical work to do to the walls etc, could be a quick win.
Rotting door. Check your contract, but this could be something they require you to change. A new door may be a lot less than you think and a short job for someone to fit it for you. Your HA / local Council may have an approved handyman service which you can pay by the hour for jobs like this.
If door replacement is too expensive, scrub, sand and paint with anti mould paint / bathroom paint.
Look at anti mould paint for other walls where it's an issue - you can also buy it as an additive to put in normal paint. Could be a few hours of work, but well worth it.
Kitchen. Apply for a new kitchen. If not, you might find kitchen cupboards available second hand for free or very cheap on places like a local Free cycle page and the handyman service may be able to do this. Failing that, shelving could be put up where cupboards should be.
Have a look for a kitchen trolley with a worktop on it if the kitchen is big enough for you to move it about - I had one in my old flat where the floorspace was 1m square, and I pushed it in front of the door when I was working in there. Added a good couple of feet of workspace for me to chop veg etc. Argos have one for £43, you might get one on Facebook selling etc for less.
Dehumidifier. Don't give up on this, it's what will keep the mould down every day. I also have reusable (microwaveable) Pingi bags in my house and car - they work a treat. I keep the bags in damp spots in the house (hallway, back door) and check them daily to see if they need to be dried out. No more mould in neither location.
Mould and mildew spray. The cheaper the better. I spray our bathroom every week, you might need to use it more regularly but keep on top of it and it's less of an issue in the longer term.
Windows. The moment it's dry outside, get them open!