[geofft]

"a" vs. "an" is based on the first sound of the word, not the first letter. You would say "an honor" but "a hair" because, while they both start with the letter h, one has a silent h and the other doesn't.

If you pronounce "FAQ" by spelling out the letters (and not like "fack"), it starts with "eff", so you should say "an FAQ." I think that's the pronunciation I usually hear.

[caf]

In particular it's "a" if the following word starts with a non-vowel sound, and "an" for a vowel sound.

[isostatic]

Compare:

  an SQL command
  a SQL command

[geofft]

I think I hear both "ess queue ell" and "sequel" for SQL frequently, but "eff ay queue" for FAQ way more than "fack."

[isostatic]

I didn't encounter "sequel" until some years after I encountered "ess-queue-ell" - had no idea what the person was on about to start with.

I guess it's one of those things that native English speakers don't even know they know. Like "Fewer tests means Less data", rather than "less tests means fewer data", or "six charming small new round green plastic tables" rather than "six plastic charming green round new small tables".

[geofft]

Or that "the" is pronounced "thuh" before consonant sounds and "thee" before vowel sounds - same rules as "a"/"an" but no difference in spelling!