Hey @Zooey,
I am just catching up here, but I will try to explain everything I can as clear as possible 
WP 5.0 introduces a new page builder (the blocks). The issue with this is that it fundamentally changes how posts and pages are created. This is what leads to the breaking of sites.
The Classic Editor already has an end of life date announced. This means after 2021 the Classic Editor will be removed from WP. By this time you have to have either put up with the new Gutenberg ways or have moved on from WP.
You can migrate your site to ClassicPress. Your host won’t stop you from using our migration plugin (details in the link).
If your theme worked on WP 4.9 then it should work on ClassicPress. That being said, I haven’t tested it but others have been able to move their themes over.
Similar to the theme. If it worked on 4.9 then it should work on ClassicPress. The only conflicts we seem to have are from plugins that monitor the code.
Yes, you can still use BackupBuddy.
As mentioned above, most plugins that worked on 4.9 will work on ClassicPress. For the future, we hope to get more developers committing to supporting ClassicPress in the future. This is something we are working on, and you can help by contacting the plugin developers and asking them to support ClassicPress. You can find out more here: Contacting plugin developers to ask for ClassicPress compatibility
Hopefully that helps! If you have any further questions we would be happy to answer them