I have to say, I don't get the problem with the previous version of Linux Mint, however, that's not helping you.
Can I make a suggestion?
Open up Synaptic (your package manager) and select Opera for installation. If you're uncertain how to do that, you either scroll down until find Opera and then tick the box - "mark for installation", then click apply or use the search facility and do the same.
Opera will be automatically downloaded for you and installed. (no reboots required).
Personally, I think it's surpassing Firefox and really is a very nice browser.
This will resolve two problems. First, if it doesn't crash, it suggests the bug is in Firefox and not Mint. Second, if it works well, it gives you an alternative until such times as Firefox is fixed.