IMHO, manufacturers do their customers a disservice by referring to the firmware in their modern computers as "BIOSes." They aren't BIOSes; they're an entirely different type of firmware. As specified on Wikipedia's UEFI page:
UEFI replaces the Basic Input/Output System (BIOS) firmware interface
With the exception of a few early implementations on x86-64, such as Gigabyte's Hybrid EFI (which I describe on this page of mine), modern EFI-based computers do not contain BIOSes, even if the manufacturer refers to the EFI as a BIOS. (Note: I use "EFI" as a more generic term; UEFI is EFI 2.x. Modern PCs ship with UEFIs, but Apple still uses a heavily-modified EFI 1.1 in its Macs.)
The problem with referring to EFIs as BIOSes is that this encourages people to apply BIOS-specific knowledge that is not applicable. They may install BIOS-mode boot loaders, use tricks intended to safeguard data on multi-booted computers, and underestimate the extent of differences in how EFI-based computers boot. Using the term BIOS to refer to an EFI may give readers a mental shortcut to understand where this component fits, but the cost is lost time and frustration on the part of users.
There is one partial exception to this distinction between BIOS and EFI, and it's a big one: Most modern EFI-based computers provide a Compatibility Support Module (CSM), which enables the computer to boot using BIOS-mode boot loaders. This is a helpful stopgap tool, but it should be thought of as an emulator -- the CSM enables an EFI to run boot loaders written for BIOS, in much the same way that DOSEMU enables Linux to run programs written for DOS. That said, the CSM does not turn the EFI into a BIOS any more than DOSEMU turns Linux into DOS. In fact, although the CSM is helpful in some cases, it creates a huge number of problems, particularly for unwary multi-booters, because enabling it can make it easy to install one OS in BIOS/CSM/legacy mode and the other OS in EFI/UEFI mode. Such cross-mode OS installations are more difficult to manage than those in which all the OSes are installed in the same mode. See this page of mine for more on this subject.
Most manufacturers switched over from BIOS to EFI starting in mid-to-late 2011 for consumer products, although I know of some servers that were BIOS-only as recently as two or three years ago. AFAIK, all consumer x86 and x86-64 computers sold today ship with UEFIs, although there may be some exotic exceptions. Some manufacturers released EFI-based computers well before 2011. All Intel-based Macs use EFIs, for instance. I've got a (now failing) Intel motherboard from 2008 that has a version 2.1 (IIRC) UEFI. Note that EFI was first used on Intel IA-64 (Itanium) systems, and AFAIK all such systems used EFI. It's also now being used on some ARM64 computers, although AFAIK this is still mostly on servers. If you're uncertain of your computer's capabilities, you may need to check its manual or peruse its firmware setup options for references to "EFI" or "UEFI." References to a CSM or "legacy boot support" may also indicate an EFI. (Note that the word "legacy" can be used in other contexts, though, such as for USB emulation of PS/2 devices.) Checking your current boot mode can also be diagnostic, but only if you find you booted in EFI mode -- a BIOS-mode boot could have happened via a CSM. See this page of mine for more on identifying your hardware's capabilities and boot mode.
I believe the above answers the first two questions. As to the third, versions can be tricky. EFI/UEFI has revision numbers, the latest as I write being 2.6. The specification document is publicly available from here, if you care to read it; and a sample implementation is available under a BSD license from Tianocore. Each firmware vendor, though, has its own version numbering scheme that's independent of the EFI revision number. Thus, the firmware version number you see in the firmware setup screens may be significantly greater or less than the EFI revision number.
One more point: Some people think that EFIs are characterized by GUI setup tools. Although such tools are much more common on modern EFIs than on BIOSes, this correlation is far from perfect. There were some BIOSes with GUI setup tools in the past, and some EFIs have text-mode setup tools. BIOS and EFI are both basically ways to kick off the boot process; their user interfaces are ancillary to that task.