Maybe some history will help...
Old style BIOS has an understanding of BIOS style partitions. The BIOS does not need an operating system in order to pick a boot entry.
Unfortunately, when we had 32-bit systems starting to see larger disk drives, many computers couldn't use larger than a 2GB disk (this is the limit of a signed 32-bit int...unsigned will actually reach 4GB). It was somewhat trivial to update applications and operating systems to understand 64-bit...this was all software. However, the BIOS is firmware and/or hardware following a standard, so nothing with a BIOS would ever be able to work with larger than the 32-bit limits. Yes, there were hacks, such as doubling the listed number of disk heads and cutting in half the number of listed cylinders, but this was just rearranging the logical view of how things are inside the disk (individual components, e.g., cylinder counts, still had limits). Making one lie to the BIOS which was counteracted by another lie to the BIOS aided the use of larger disks (the penalty was that defragmenting no longer really was optimum performance...the internal concept of how the disk was arranged became fantasy).
So someone thought to let the operating system do more. UEFI in part takes some of what was in the BIOS and instead puts it in a UEFI metadata area at the front of the disk. Now if the operating system were one day updated to support something like 128-bit, in theory the same motherboard will still work via software updates (you wouldn't need to replace the entire motherboard). Some of the BIOS capability was transferred to the disk for UEFI and the soldering iron became less important to upgrading disk size (that's only half joking!).
When your disk is UEFI-capable, and also BIOS capable, it means it works with a wider range of disk partition schemes. As long as your operating system installer cannot understand newer UEFI, then installing a UEFI partition scheme will only lead to the operating system failing to load. My older Windows 7 is an example of something forcing me to use BIOS mode because of the installer DVD.
If your Windows install was via BIOS, there is neither need nor reason to worry about UEFI mode. You can buy a newer operating system and key and install from scratch if you want to. You only need to do this if you plan on installing into a C: partition too big for BIOS. In some cases, even if the BIOS can't see an entire partition it will still work if everything needed for boot stays within the 32-bit limits.
What have you been told about UEFI which makes you believe it would be an advantage? It isn't faster, it's just easier to update as hardware changes.
On the other hand I have found Ubuntu's installer to not work correctly when mixing BIOS and UEFI. So if you are dual booting older Win 7 and Ubuntu, then you might have a problem even though the live DVD works (that's Ubuntu's fault).
Btw, having a password in the BIOS is no different for old BIOS versus UEFI. Physical access resetting this will still get around it and the password is not within the bootloader itself (or rather enforcement of a typical BIOS password is not in the boot loader...the operating system itself can have a password in the boot loader, but this isn't what the BIOS/UEFI deals with). You might want to use some form of disk encryption if you are worried about a rebooted system being compromised.