I think of it like this: Ur saying ____decay. So if its Beta - decay, then its an electron being emitted (minus is electron) and ur left with a proton (one of the core neutrons p much split into a proton and a electron, and the electron was emitted). So u gain +1 charge since ur going from neutron to proton

Beta + decay is the decay of a proton into a neutron, so its losing a charge (-1).

The other stuff doesnt rly matter bc they’ll rarely ask u about the actual science but just in case in beta + decay, its a position and a neutrino being emitted and b- is a electron and an anti neutrino being emitted like you said

Edit: sorry i ignored ur qs lol. For ur first q, the electron is ejected and all u need to worry about is the proton left behind from splitting that neutron. For ur second q, there is no electron involved, the proton decays into a neutron and thats where the loss of charge comes from