1. When clubs are customized for someone, is the shaft the only thing adjusted?
No. Lie (how toe up/down the club sits at address) may also be adjusted. You might want to have lofts checked as well.
2. What should be tested when he does my clubs (besides height)?
A static fitting should be the place to start. Wrist-to-floor measurements, hand size, etc. This should be followed by a dynamic fitting - swinging the club with marking tape, checking posture, etc. Your swing speed should also be checked, but not with your knowledge, ideally. When most people know they're having their SS checked, they often swing harder than they would on the course,
3. Any recommendations for shafts?
No. There are a ton of great shafts out there, and each one plays different. I
would have them frequency or deflection matched, and spined. (This is known as shaft puring). This will go a long way to having the
clubs play more consistently club to club.
4. What flex would I be looking at?
With a 3 or 4 iron from 150, that sounds like a highly flexible shaft is your goal. But the letter stamped on the shaft is likely irrelevant, as one companies' R flex is another companies' A flex, and yet a third company may have the same flex labelled S.
This is the importance of a good clubfitter - s/he can suss out your requirements, then set up your
clubs to best match you. Don't be ignorant - there is a price to pay for well-fitting and well made
clubs. And while OEM's may make great HEADS, they don't assemble their
clubs well.
Just my .02