The problem is caused by the command below

mkfs -t vfat /dev/loop0

/dev/loop0 is the whole disk, and /dev/loop0p1 is the partition.

The command make a file system on the disk, thus overrides the disk’s partition table.

I guess that it is the partition on which you want to make a filesystem.
The right command is

mkfs -t ext2 /dev/loop0p1

We prefer ext2,3,4 to fat32 on linux.

I see. Thanks! I used kpartx to map the partitions in /dev/mapper. If you know of a better way of doing what you suggest, could you please let me know?

I was hoping to use ext4, but I wasn't able to grub-install to a loopback device. When I try to, I get the error:

> grub-install: error: disk `lvm/loop1p1' not found.

From a searching around, it looks like this issue has been visited recently by the developers:

https://lists.gnu.org/archive/html/grub-devel/2015-05/msg00011.html

So I wasn't able to get it to work. So instead I've been using syslinux, which I believe requires FAT, rather than EXT. I read about extlinux, but from my reading, I've gotten the impression that syslinux has more history. So I figured it would be easier to find useful material for syslinux on message boards.

Thanks again for all your help! I hope that at some point I'll be able to do more, such as customize the ram disk, the init system, and figure out how to get the system switched over to a root file system on a disk.

-Patrick