You can ask Luna to make your dream address private.
People can still visit your old town dream address of it's public and Nintendo hasn't erased it.
You can visit your own dream if it's a different dream address. Such as Nintendo erasing your old dream address and asking you to create a new one.
Yes you can have multiple dream address if it's an old dream address that Nintendo didn't erase.
Source: back in June Nintendo did a huge server update and got rid of all old dream address. I had a dream address from back then and Nintendo made me change it but it is still around. You can search for "Harvest" and two "Cherry from Harvest" will show up. One is my town back in June and one is my town now.
First, yes, you can tell Luna to hide your DA on your card so that others can't see it, but yes, if they still have the number they can visit it or it can be found from random assignment or through searching for town or character name.
2)there is some weird mechanic that resets DAs as time passes.
when you go to update your dream, Luna may tell you that your DA has changed.
when this happens, you will now be updating a new DA while the old one will stay in limbo until enough time has passed since the last time someone visited. you can't update it, and it won't be recognized as your town anymore, so yes you can visit your own old address as it was the last time it was updated.