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Not that I know of -- there are just browsers that don't send out some stuff because they don't have the capability to detect it. You could do some more header-stripping with extensions and proxies, but in the end, like with cookies, this is stuff that a website might need to actually work properly.

The TOR browser if probably your best bet for this, even if you don't use TOR to browse.

Yes, but it is trivial to distinguish usage of Tor browser as commonly distributed and Tor browser in TAILS, by default one comes with an additional plug-in.

To do this well, you have to take special care with how exactly you obscure them. If your browser refuses to report those values, or sends junk values, then you might actually make the problem worse. It's the internet version of this: https://xkcd.com/1105/

Firefox has various privacy.resistFingerprinting preferences that can be flipped by extensions (or manually). Expect some sites to break though.

Edit: Oh, apparently there's built-in UI now: https://blog.mozilla.org/firefox/how-to-block-fingerprinting...