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the registration page is not templated, it's hardcoded unfortunately.
editing is pretty simple to an extent depending on exactly what you require it to do.
it is quite possible to add a 2nd page to the registration process, but it would definitely be easier to split the existing page by a horizontal rule as you suggested and have the extra fields displayed in a different colour.
of course you create the fields using the profile admin create field function.. and then you could probably add a different css class to those fields (not tried it, but is possible i'm sure) the work i did on the coppa registration involved lots of work on the registration files, so i'm quite familiar with it in some respects.
regarding logging user in after activation, i think it could be done, but i think it isn't for a reason (altho a dev maybe able to say more about that) i'd stay with it how it is at moment in my opinion..
but yes it would be possible to do the other things you ask.