I can't comment on private mode, but I run Firefox 101.0.1 on Linux Mint 20.3 cinnamon without any problems or noticeable lock ups. I assume you routinely apply all the Mint updates - usually at least once a day! - which will include the Firefox update. A very few web sites don't work properly with Firefox so I have a Chromium on my machine as an alternate. Also for a few weeks the Simple Flying web site was blocked as being insecure even though it was https, but whatever it was is now sorted