I was trying to restore a time machine backup but then messed everything up as I had erased the wrong disks and was just being a downright idiot for erasing drives. Now I can’t install a fresh OS or restore time machine. Is there any way I can reformat the drives in disk utility to be about to reinstall a new OS? Here are the images:
From your third picture, that's the drive you need to format.
Click the drive name, as you have in that image, then click Erase [top centre] & supply a name. The rest will automatically be set to the correct parameters - Mac OS Extended (Journaled) & GUID Partition Map.
Apple Partition Map is a very old format type, for 68k & PowerPC Macs, not in general use any more.
On installing Sierra the system will likely change that Mac OS Extended (HFS+) format to APFS, but that will be automatic & need not concern you at this juncture.