By default if your the let's is your computer you don't need admin to install it unless the Admin/Owner account has password set then you can't install without the admin entering the password to install the software. So whom is the owner of the computer your trying to install it on.

I clearly remember that around June or July this year, there was a .zip or .7z version available (maybe another format), which allowed you to run Firefox directly without needing admin credentials.

Now, without admin privileges, I can't install the .exe or .msi versions, which is quite frustrating. Again,

1. Is there still a no-admin-rights version available? 2. If not, why was it removed? 3. Any plans to bring it back?

This is a link to older and newer Firefox but also has different language version so make sure to match the one your looking for as well. Latest is 131.0.3 on the site.

https://archive.mozilla.org/pub/firefox/releases/

I clearly remember that around June or July this year, there was a .zip or .7z version available (maybe another format), which allowed you to run Firefox directly without needing admin credentials. Now, without admin privileges, I can't install the .exe or .msi versions, which is quite frustrating. Again, 1. Is there still a no-admin-rights version available? 2. If not, why was it removed? 3. Any plans to bring it back?

Mozilla has not had .zip versions for Firefox Releases since Firefox 1.0.1 Released twenty years ago back in 2004. The Firefox Releases used to have .zip alongside the setup .exe. When Firefox 1.0 Release came out the number of Firefox users skyrocketed and when 1.0.1 was released many people thought they had to install it over the 1.0 in order to keep their settings. The problem was this was ended up causing crashes due to mixing the .exe and .zip versions so Mozilla discontinued the .zip version starting 1.0.2 Release ever since.

The full Firefox setups .exe for Windows is compressed by 7zip so you can technically extract it and use it that way.