As to how to type other people, I think you can use a few methods in combination. Central to all of it is listening to how they communicate because it gives you clues as to how their mind operates.
- Seek to understand/guess their temperament: SJ, NT, SP, NF; it's pretty imperfect but I think you can usually narrow it down to two of the four
- Look for evidence of the 8 cognitive functions in their communication and in particular, what cognitive functions appear to be utilized and how commonly are they utilized; it's a lot easier to recognize the extraverted functions but there are clues as to whether or not they prefer Fi vs Fe or Si vs Se or Ni vs Ne or Ti vs Te.
- Try to figure out which function is dominant and which one is auxiliary; I admit that I look at I/E to help determine this but it's not perfect as you stated above
Between those three, I can usually get a decent idea. I just talked to someone on the phone today and could pretty much tell they were an NF right off the bat. I'm not sure which one - probably INFJ. It's a guess.
So what I do is to come up with some guesses and then look for evidence to narrow it down. Still, I find it difficult.