Is there a realistic way a person having an old computer and cheap (but not free) electricity can actually mine monero equal to some amount which can be used to donate to good service providers or purchase services?
I keep hearing about low reward to effort ration, but can I get a respectable amount in let’s say a year without having to deanonymize myself by going to a Centralised exchange?


No.
I mean, check https://www.coinwarz.com/mining/monero/calculator and see for yourself, but I don’t think so.