I am moving from windows to linux, My profile folder is valid as backup to restore in Linux?

I think yes, but also, use sync.

Yes. I wrote down the procedure a few weeks ago which may come in handy for you as well: https://www.bahmanm.com/2023/07/firefox-profiles-quickly-replicate-your-settings.html

Yes. Copy the [random gibberish] folder itself from %AppData%/firefox into the .Mozilla/firefox folder.

Aren't they synchronized with the Firefox account?

Pretty sure only the filesystem will change - so if you are synchronised as a backup, just zip up that folder and pull out what you need for the new install. I had no issues re-installing with BTRFS from ext4 and restoring a backup file a few months back.

Also, I'd say definitely stop using these for passwords, if you use Bitwarden or something similar then you can have the same stuff for your phones/tablets/computers everywhere that don't rely on local files.

If I start a session somewhere outside my home environment, I can pull up Bitwarden and log in with no issues - nothing saved to the browser and no conflicts between phone/desktop etc (e.g. icloud passwords clashing with ones I use on my desktop - I use Bitwarden on an iphone too).

I haven't done it recently (no Windows since a few years ago) but it should work.