Will PureOS 10 allow a self-updating Firefox?

I’m ready to upgrade, but I’d like to know if I can still install my own Firefox, Bitwarden and other apps like I can in version 9.

Not sure I understand the question correctly, but if I do, yes you can. I’m running PureOS 10 and have my self-updating firefox installed, as well as several other packages that are not in the standard repos. Bitwarden, even though not installed, could, e.g., be installed from flathub.