I don't know how "legal" it is to buy a bike and not to transfer it to your name. I know that you can do it, people do it with illegal bikes, meaning that those plates and the registration are both fake, altered or who knows. If you want to do it just understand that in case of an accident you will be FULLY LIABLE, even if it is not your fault, and your insurance will not cover the expenses, of course not to mention the legal actions you would be facing.
I think you are totally right about the registration, meaning that you have to be registered at the nearest police registration office within the area you are living.

Sabine, I think you are wrong, if the bike is not registered to your name the police can't fine you unless they stop you, and if they stop you, then you wouldn't be able to say that it was somebody else driving. They simply cannot find you if your vehicle is not registered in your name and residence, right?, that is why people hire agents to help with the procedures and paperwork, legwork, etc. Again, that's only if you want it legal.

There are some posts here about registration agents, maybe you can contact one that can help you to solve your concerns

If everything is registered properly, even if you are riding outside your resindence's province, you should be ok, unless you are riding on a highway (most of them are forbidden for motorcycles) or in a city with motorcycle restrictions.

If I were you, I would make a list with more or less the places you want to visit and let the people that post in the forum tell you about the possible restrictions you may face, users here are very glad to help.

Cheers!