Would old characters stay between map changes?

No. Part of the map installation is a complete wipe of the old database.

Ive done it before, and it worked for the most part. But an issue arises when items that are regional, horses, or preparations are kept in the DB over a wipe. Basically the feature ID of these items start to conflict and causes them to be dropped in a bag and deleted from the inventory. I.e if you were putting up a horse, and someone across the map was getting a regional board, they'd be assigned the same feature ID. The db would see this as a duplicate and delete the duplicate. In game this ends up being the horse dropping into a bag on the ground, with the bag being empty after the horse is deleted.

Overall its generally unadvisable to do it but if you want to you need to export these tables in a SQL file
character
character_blueprint
character_effects
character_wounds
containers
items
item_effects
guilds
guild_lands
guild_standings
heraldries
objects_patch
skills
skill_raise_logs

From there you'll install the new map, once that is up and running you run those SQL files into the DB.
Youll then have to go and do a map refresh to get rid of the claims and houses that end up back on the map
After the map refresh completes you need to go to the tools and do a database clean up and click all the boxes (this is to mainly get rid of the guilds)
From there it should be good to go, but remember, there are issues with doing this and I highly advise against doing it unless absolutely needed