I think it means to not care enough to do something- to feel too lazy for it, for example. But let's wait for some native English speakers to respond :)

Correct- not to bother to do something literally means you weren't bothered (didn't care) enough to do it. So if I don't bother to call my girlfriend she might get upset.

To not want to do it, to not care to do it. Could be due to laziness or just believing it is not worth it to do something

I think it means either don't even try doing something. Or it's ok you don't need to do anything/it.

bother means disturb or take the trouble stop bothering your dad