On a normal hard disk installation of most any EFI-based OS, you'll have, at a minimum, one FAT EFI System Partition (ESP) and one partition for the OS itself. The ESP holds a boot loader for the OS, possibly along with files to support the boot loader (fonts, configuration files, drivers, etc.), and possibly even the OS's kernel. The OS partition holds more-or-less the same OS files you'd find on a BIOS-based installation of the same OS. Depending on the OS, you might have additional partitions, too -- data partitions, a swap partition, etc.
There can be exceptions to this rule, particularly for installation media or emergency disks. For instance, you could put the whole OS in the ESP. Also, most EFIs are happy to boot from partitions that are not ESPs, so you could just have one big non-ESP FAT partition, as you've got. This can work fine for an emergency disk, but I wouldn't recommend setting up a regular OS installation in this way; I'd use a separate ESP and OS partition.
Note that a standard EFI can read FAT, but cannot read NTFS, ext2/3/4fs, HFS+, or any other filesystem. (Apple's EFI can read HFS+, and so can read its boot loader from a Mac OS X root partition rather than from the ESP, but Apple's EFI is the exception rather than the rule. A few EFIs also have ISO-9660 filesystem drivers -- but again, they're exceptions to the rule.) Because FAT is the only filesystem that's guaranteed to be readable by EFI, an attempt to build a boot disk that does not include a FAT partition is doomed to failure, except of course when used on those unusual EFIs that support additional filesystems.
I can't provide a procedure to set up a Windows emergency disk to use separate EFI and Windows partitions, since I'm more of a Linux person than a Windows person. Unless you run into a specific problem with your approach, though, I'd just stick with it; at least you know it works.
Error 0xc000007b may relate to mismatch between 32- and 64-bit, so may be caused by 32-bit grub4dos trying to boot a 64-bit OS.
The grub4dos latest release dates from 2009 and knows nothing about UEFI,
so shouldn't be used.
You should probably start from scratch and use the tool UEFI MULTI.
The purpose of this tool is described as :
Tool to format USB-stick for Booting with Boot Manager Menu on BIOS or
UEFI computer and Tool to make USB-Stick having two partitions - FAT32
Boot partition for WIM or ISO and NTFS System partition for VHD.
Option to Install Grub4dos in MBR BootCode, which allows BIOS computer
to boot directly from USB with Grub4dos Menu. Option to make Boot
Manager and Grub4dos Menu on UFD to boot UEFI + BIOS directly from USB
with Boot Manager Menu.
This link describes the procedure of how to create the USB disk.
The procedure is much too long to reproduce here.
Although this tool claims it can do what you want,
I have no personal experience with it.
As regarding your question about how can one disk work for both BIOS and UEFI,
this magic is probably achieved by using a Hybrid MBR,
which is a format of the disk that looks as if it is both MBR and GPT.
This is possible since GPT by design does not use the disk boot sector used by MBR.
The size of a Hybrid MBR disk is limited to 2 TB, the maximum size of an MBR disk.
Best Answer
A quick primer on EFI/UEFI:
Normally, if you start from a completely blank disk, OS installers will create the appropriate partition table and partitions automatically. If you want to set up unusual partitions, it's critical that you understand these issues and know how to create suitable partitions (including the ESP, if you're booting in EFI mode) yourself. Note also that the partition table type (MBR vs. GPT) is important -- as noted earlier, MBR is tied to BIOS-mode booting and GPT to EFI-mode booting, at least for Windows.