My situation with my landlady is pretty similar. She’s also quite slow at fixing stuff and I’ve mostly been communicating with her through my ex-girlfriend who used to live here. Recently (i.e., since yesterday) I’ve been using ChatGPT to talk with her about a current problem with one of my AC units and a water leak in the bathroom that’s been going on since forever, checking the results with Google Translate and deleting unnecessary bits, and that’s been working out pretty well. Probably easier than having a three-way conversation too. Maybe you could try that.
I definitely wouldn’t complain to her about something minor like a broken AC remote, especially if you’ve already got two one others. At least she seems willing to pay for the AC cleaning (I understand that not all landlords are). Personally I’d probably just buy a universal AC remote from Shopee and, if you want, ask the landlady if she’ll pay for it.
I have dealt with some minor issues in the apartment myself (adding a corner brace to a sagging kitchen cupboard, replacing the tubing for my drinking water tap after it burst and leaked everywhere, and buying a new gas regulator for the gas bottle guy to fit at half of the usual price). I find it less hassle to do these things myself than bother the landlady and wait for a chabuduo workman to come out and not really fix the problem, and I think the landlady is happy for me to deal with it because it’s cheaper for her. I think her perspective is just that it’s an old apartment she’s not too keen to sink lots of money into (e.g., to tear off and replace the kitchen tiles to properly replace the broken drinking water tubing), and I guess I can understand that.
For the bathroom leak issue I mentioned, that’s been going on for at least two years. Apparently water is sometimes leaking into the downstairs apartment, so it’s more of a problem for them than it is for me. Every time a workman comes (which has probably been at least ten times now), they seem to just do a short-term fix before the neighbors start complaining about it again a few months later. The guy who came yesterday just showed me how to turn off the cold water supply to the water heater (I could have figured this out myself, but anyway that’s not a fucking solution, even if it works, which it didn’t because it’s still leaking, and I told them as such 
). I think one of the pipes in the wall is broken and needs to be replaced, so it’ll be a pain if that ever happens.