Copying the profile folder should do it
You should also copy profiles.ini (which indicates the path of the working/available profiles)
Generally speaking, this should also work for other forks, but it might depend on which versions the forks are based on. If they are too behind the version that the profile is from then there might be "forwards compatibility" issues, for example in the way specific files/databases are structured (but maybe not, this is just a guess).
Also note that since forks tend to have different default values for some settings then if you didn't explicitly set them through a user.js file or directly in prefs.js (or another method) then you would get the default from the fork instead of the one from the main version.
Yes, it will copy everything related to that profile. The passwords are stored in the key4.db file so it shouldn't be copied in that situation.
https://support.mozilla.org/en-US/kb/profiles-where-firefox-stores-user-data#w_what-information-is-stored-in-my-profile
Then there's also the sync feature which might import the passwords even if the file has been deleted, so the sync needs to be disabled on the work pc.