Character progress is separate from world progress. No issues unless the server has a mod locking you to that through a mod.

World progress on a server is locked to the server. I think there may be some way through third party programs to convert it? Not sure, I did want to copy one I was playing on and the server owner never figured it out.

But in the base unmodded game you can jump between worlds and your character carries all his stuff and all xp gained for that character is added.