I don't agree with compulsory voting but agree with everything else you said.
Same. I'd have no problem with compulsory registration, though I'm sure certain anti-govt and paranoid types on both (all?) sides would.
In Canada there is essentially an "opt-out" model of voter registration where government agencies by default share information with the national register of electors, but you can ask to get yourself removed, and you can check a box on your income tax form, drivers' licence applications, etc. if you don't want them to send the info. This seems like a good balance between making registration as easy as possible and the traditional Anglophone dislike of mandatory government tracking of domestic movement.