I need your cleaning tips- bathroom

[whataboutbob]

Yesterday I visited my brother. For background, he lives alone after our dad’s death and has some mental health problems . He was offered sheltered housing but refused. The hygiene levels in the home are not good. I spent over an hour in his kitchen unblocking his sink, then cleaning it and doing his washing up. I took a load of stuff to the dump and cut back the jungle in his front garden.
I noticed the bathroom but didn’t have time to tackle it so will return next month. It has thick layers of what looks like limesc ale and scum all over the sink and the bath. How best to remove them? What products work best? The bath is plastic I think. Any other general bathroom cleaning tips gratefully received.

@neighneigh point taken I won’t mix chemicals, I’ll rinse off in between the different ones.
@CAAKE. I know where to get hold of citric acid ( Indian grocery stores) I use it to make elderflower cordial. Will try it as a cleaner, good tip.
@zzzzz thanks for the tips, really nice ideas .I took a pic of the toilet cistern and I’ll be taking it to my plumbing course next week hopefully the tutor will be able to suggest how to tackle it. I am hoping some improvements will boost him a bit. It’s genuinely hard to tell whether he notices the dirt or not. I suspect he might minimise to himself and others how bad it is because he’s scared services will try and get him to move out ( he’s terrified of change). He is on the autistic spectrum so is hard to read. Can’t help hoping a nicer environment will give him a boost though.

@GreenTulips from the pic on my phone I think your instructions re fixing the loo handle are correct.

The black Harpic toilet cleaner/descaler is fantastic if it's a build up of scum and hard water!

and scourers - I like those that look like tangled wire

No offence to whoever suggested using these...but OP...I used them once when we bought our first house, trying to remove the limescale from the toilet. Made a right old mess. They left loads of big black scratch marks on the porcelain which wouldn't come off. The whole thing looked worse than when I'd started.

Harpic 100% limescale remover works if you leave it overnight for 3 nights running and no scrubbing required.

Just an update. Went back yesterday. To clean bathroom ( sink, bath, toilet) I got hold of some Ajax powder off Amazon. I shaked it liberally over the units, then went into town with him for tea. When I got back I scrubbed hard ( unfortunately I didn’t have the best of sponges as I had to rely on his old soft ones) and even used wire wool on the toughest grime. That shifted most of it. Bro was pleased, even saying “ it looks like a hotel “ ( realistically, still not a hotel that would get more than 2 stars on tripadvisor, but a big improvement nonetheless).
I found the loose loo flush was easy to fix- just lifted up the cistern lid, and tightened the screw which sits against the internal cistern wall. Next up, his downstairs loo which needs a clear out and a clean. And a plumber as it no longer works!