Do hard drives need a GUID partition table (GPT) to boot in UEFI mode

My first suggestion is to upgrade your firmware. Check your manufacturer's Web site for such an upgrade. (It will probably be called a "BIOS update" or something similar; manufacturers usually call their EFIs "BIOSes," although IMHO this just creates confusion in the long run.)

My second suggestion is more of a comment: The Windows 7 disc is a bit weird when it comes to EFI-mode booting. There are various Web pages that describe this and provide workarounds, but the only one I have bookmarked is my own page on DUET. The section "Installing Windows Under DUET" describes the procedure, but it's somewhat DUET-specific. A Web search might turn up something that's more directly applicable to your situation. Of course, if you're having problems with other EFI-mode boot discs, too, the Windows 7 issues obviously won't apply to them.

If these suggestions don't help, I recommend you try using my rEFInd boot manager to detect your CD/DVD as an EFI-bootable device. You can theoretically do this without mucking with your hard disk by using rEFInd on a USB flash drive, but if your firmware is flaky about booting external devices in EFI mode, you might need to install rEFInd on the hard disk. If you install rEFInd on the hard disk and it doesn't work, you might try installing the ISO-9660 driver that comes with rEFInd. The ISO-9660 driver probably won't help with the Windows 7 disc, but it might help with some others.

Yes. It’s also not about GPT or MBR partitioning schemes. It just needs to be FAT32 (could work with other filesystems too, depending on what the actual UEFI implementation supports) and have the bootx64.efi file at the right location.