Sounds like storage issues, although I can't comment on the broken apps in the second post. Sounds like filesystem issues there... you should probably do an fsck.
But, first things first. If you can boot and open Timeshift, go to Settings/Schedule and reduce the settings in there to minimise the number of snapshots it keeps.
(Of course, if you can't, don't bother reading on; it'd just be a waste of your time.)
In an absolute crunch I'd set them - from top to bottom - 0 Monthly, 1 Weekly, 2 Daily, 0 Hourly & 0 Boot, although you should keep as many as possible.
Close settings and then go back to Timeshift's main menu. Select & delete all of the snaphots with a tag of 'O' except one or two of the latest. Then work through the rest to match what was set in the Scheduler. eg. For the example I provided above delete all marked M, all but the latest tagged W, all but the last 2 tagged D... you get the idea?
If you want to keep an hourly or Boot snapshot, make sure it's NOT one the latest few - which may be corrupt - but timestamped BEFORE you started having this problem.
Obviously, this will free up the space used by the deleted snapshots.
My next step, personally, would be to boot into Live USB/CD and do a filesystem check on your drives. It's not necessary to use Live USB/CD but it can avoid some complications. If all goes well, then reboot as per normal and see what - if anything - still needs "fixing."
Then go shopping to look at buying more storage!
Don't forget to reconfigure Timeshift to give you a good backup solution afterwards though! The suggested settings are close to bare safe minimum...