Unfortunately there's no newer Firefox package in the stable repos at the moment, but I found a way to use newest Firefox ESR (currently 52.1.2) on my Devuan Jessie without a problem. I will explain that later in this post.
(Note: New versions of Firefox (52 and up) require PulseAudio for audio playback, see here.)

Q1. You can check it this way for example:

# apt-get update
$ apt-cache search firefox    << this will show you the list of packages with 'firefox' in their names
$ apt-cache policy firefox-esr    << this will show you installed version (if any) and versions available in the repos

Q2. You should use:

# apt-get install -t jessie-backports package_name

That's probably not the "best way to install latest version of Firefox", but my solution was:
1) I've downloaded Firefox 52 ESR from here > https://www.mozilla.org/en-US/firefox/o … tions/all/
2) I extracted it and copied 'firefox' folder to my home directory (for example /home/my_name/Applications/)
3) I changed default web browser in Preferred Applications settings (exo-preferred-applications), choosing "Other..." The path should be something like this - /home/your_name/Applications/firefox/firefox "%s"

You can also add individual ".desktop" entry for it in the ~/.local/share/applications/ folder (that way it will show in the main menu) or you can just use "Web Browser" entry (exo-open --launch WebBrowser %u) to open it. You can use GUI tool 'menulibre' for adding desktop entries.

And that's it, now I'm on newest ESR branch, it uses my settings from ~/.mozilla/ without a problem, it even auto-updates, everything works fine. Well, almost... Still, from time to time some links want to open in the "older" Firefox 45, because the newer one is not registered as a default browser system-wide (it doesn't show in the update-alternatives --config x-www-browser). I didn't find a way to do it 100% correctly yet. Maybe it should be placed somewhere in the /bin or /lib folders instead of /home?
// EDIT: That issue was solved by smoki one post below. Thanks!

If something is unclear or you have more questions, I'll try to help. Cheers.