Apple_Boot partition created on external drive? I used Disk Utility to partition my external drive into four partitions: two in Apple file system (called H1 and H2) and two in FAT (called F1 and F2). However, I found by diskutil list that an Apple_Boot partition called "Boot OS X" is automatically created:

0:      GUID_partition_scheme
1:                        EFI EFI
2:          Apple_CoreStorage H1
3:                 Apple_Boot Boot OS X
4:                  Apple_HFS H2
5:       Microsoft Basic Data F1
6:       Microsoft Basic Data F2


Why is there an Apple_Boot partition? Does it mean that now I can boot a Mac using this external drive? But the size of this partition is much smaller than my recovery partition "Recovery HD" on the internal drive, so I don't think this is a full copy of the recovery partition.

I want a "clean" partition without introducing Apple_Boot or EFI. (I remember from the old days there was a limit on the number of primary partitions, so having six partitions makes me feel uncomfortable.) To do this, can I use Windows to partition my external disk, and then use my Mac only to format H1 and H2? Can I still use H1 for Time Machine if I do so?
You created one HFS partition, and one Core Storage partition, on which an HFS partition resides. The difference is that a Core Storage partition can be encrypted. I've never found a use for the Apple_Boot partition, although it is replaced with the recovery partition when you install OS X. You needn't worry about running out of partitions. The limit is ridiculously high these days. The EFI partition is part of the GUID Partition Table format by default, and should be kept. Neither Apple_Boot nor EFI take up much space, so I'd shy away from deleting them without a good reason.