When my retired mother applies for visas, I (I do the application for her) never chose Unemployed. Always "retired", and if there's no such option, then Other and write retired, if possible. I think unemployed comes with a negative stigma, and also, both my mother and you get a pension, so saying retired is not lying.
It's not black and white. In theory, as per the law, some overseas income is supposedly to be taxed IF meeting certain conditions, such as being remitted to Thailand within certain period. In brief, blanket affirmations such as "all overseas income is to be taxed" or "no overseas income would be taxed" are both incorrect generalizations. Then, double taxation treaty with specific countries also play a role.
not needed if one is a remote worker. I get paid my monthly salary in my home country bank account. I'm not moving (nor I need to) my money from that local account to Thailand. What for?
Unpopular advise: offer him/her money, and he/she will willingly do it. Should you originally have to pay for it? Of course not, but the only person that would face problems is you (please don't say that the landlord will be fined, we all know that it doesn't work that way).