katers this sounds like your web host isn't doing a good job. Things do happen, but the backup should have been able to restore everything other than any changes you might have made since the last backup.
Also there's never a reason for a web host to write an email blaming you when something goes wrong with their server.
I think you're making a good call looking for another host.
That doesn't help you get the site back though. If you didn't already have a backup then you probably do have to rely on your host to get things back as much as possible, but there are some things you can try.
Try the
Internet Archive. Towards the top there's a search box for the Wayback Machine. If your site has been online a few years it's possible they have some of the older pages. Unfortunately they won't have newer pages and they may not have the pages you're missing, but you might find some content that's possibly lost.
Another place to check is Google. Search for info:
www.yourdomain.com/filename
That's the full URL of one of your missing pages. As long as Google has indexed that page they will show a result and some links below. One will be a link to the cache of the page which should show you what the page looked like the last time Google indexed it. Grab the page fast, because if Google comes back again and sees something different at that URL the cache may change.
One more idea is to check your own computer. If you had visited the site, especially the missing pages recently they might still be in your temporary files folder on your computer. I once accidentally deleted a file I was working on and found a copy in the temporary folder which saved me from having to recode the entire page.
Hopefully your host will get the entire site back up for you since these other ideas aren't guaranteed to work.
In the future make sure to regularly back up your files. I like to keep a copy of all the sites I work on on my own computer as well as on some backup drives I have. At the very least make sure you keep a copy of what's on the server on your computer.