First issue is repairing/preparing the root file system so it can be safely copied from, let alone physically altered.
If you have the space to create another partition, you do not need to resize the root. You can put the contents of one of the subdirectories on the new partition and mount that partition to that subdirectory mount point. So for example, you could copy everything in /usr to the new partition and then mount that partition (in fstab) to /usr.
Whether you take this approach or that of resizing the root partition itself, you need to reclaim some space and do a file system check first. When a partition gets full there can be faulty writes and consequently, reads. So it’s dangerous to try resizing or even copying right now. Even a full backup now may be corrupted and hence unusable.
To reclaim some space, you can (1) delete files out of /tmp. In YaST /etc/sysconfig Editor, look at Cron under System. Note the Max Day, Tmp Dir, and Owner. Set that to 30, /tmp, and blank. After cron next runs, you may have bought several hundred MB.
Then (2) use the tune2fs -m command to reduce the amount of reserved-blocks space. The default is 5%, which typically is plenty more than needed. Set it to 3%. Frees another couple hundred MB.
Reboot. See if df shows space available. You should be able to run e2fsck with the -f option now. Then reboot again.
Now take a look again in YaST Partitioner. Still an error?
Now back to the original question again re resizing root. If there is a problem with the partition table, trying to fix it may make the system unusable. And especially trying to resize it. There are good tools like TestDisk, but there can be unforeseen issues e.g., due to what other software has done with the table (notably Vista). There are lower-level tools like disk editors that enable directly writing to the table, but this is very serious and only for experts. IMO, your best solution is a separate sub-directory partition as described above. At a later point you could copy the root to other storage, delete/re-create the partition, copy back. But again, this means changing the table; if there are still indications of problems with it, you may lose the whole disk. There’s a good chance that if you just leave it alone, have reclaimed space otherwise, and the file system is in good shape again, that you’ll be OK.