High Sierra won't install: for the boot disk it says: "This disk cannot be used to start your computer"

Solution 1:

You must turn off filevault before install HS...

Solution 2:

My wild guess would be: remove rEFInd from the EFI or replace your current EFI partition (disk0s1) with a new one. Afterwards first backup and then remove any additional partition after disk0s3 (but not a recovery partition) and any second logical volume and finally expand the CoreStorage LVG to the full size of either 512 or 768 GB (depends on your SSD).