The ELF/Dwarf standard does not set a standard output file extension. Common extensions are .elf, .axf or .abs. To verify the format of the file, you could open it in a text editor (look for ELF at the beginning) or use the readelf command (see Converting a Raw Binary File into an ELF/Dwarf File for Loading and Debugging | MCU on Eclipse ).
Because ELF/Dwarf is standardized (there are different revisions of the standard), it makes the format interchangable, so in theory you can produce and consume the files with different sets of tools. In my experience the GNU tools are doing a good job on this. But you might run into some issues (especially with debugging) as every standard can leave some room for interpretations, and in most cases tool chains are tested with what they produce, and not with mix-and-match combinations. So technically you will be able to debug axf (or any ELF/Dwarf) files with Keil or vice versa.
I hope this helps,
Please see the following thread for more information about the axf format:
About your last question, I don't think it is possible to debug an axf file compiled by gcc.
Hope it helps!
Technical Support Engineer