Apple - Choice of Scheme when formatting USB flash drive in macOS

In virtually all cases, you want GUID Partition Map. Only choose a different scheme if you have specific needs that require that scheme. GUID Partition Map provides the best compatibility and is the most current scheme.

Without knowing what the error is, I can't say why you're unable to erase the disk. The top level item is the disk itself, whereas the lower level items are partitions. When erasing a specific partition, you're only changing that partition, not the whole disk. Since the scheme is for the entire disk and not one partition, it doesn't make sense to have the scheme show for a partition.

Sadly, Disk Utility has been made progressively worse in recent versions of the Mac OS (macOS or OS X or whatever).

Usually, as mentioned already, the correct scheme is GUID. You only need MBR if you will be talking to the drive using older versions of Windows (XP and earlier if I remember correctly), and only need the old Apple scheme when using early versions of Mac OS (pre-OS X?).

However, regarding your inability to format the 'drive' rather than the 'partition', try selecting the partition button along the top of Disk Utility. That should allow you to create a partition on the drive and set the partition scheme. Then select the partition on the left hand side and format it using the filesystem of your choice.