No. You should not have to redo any thing. The most important part to confirm are file paths. Although many of the file paths in the config are relative to the $INSTALL_DIR, occasionally, you could have something that is absolute. For example, consider you were using D: previously but on the new machine it is E: drive. In that case, you will have to do a file replace.
Yes. Xeams is supported on both Server 2016 as well as 2019.
Contact our support via email if you run into problems after moving the files.