I assume that limiting a pitchers innings limits how much he develops right? 40 pitchers per start won't help as much as 80 (assuming his stamina is sufficient for that)?

Assuming playing time does affect development generally, does it affect specific areas based on the type playing time? Would a player who plays only against righties improve more than normal in vR but less in vL?

Some believe it's innings/AB while others think it's appearances.   I don't think we know for sure.

I've seen nothing to indicate only hitting vs. lefties would only develop VL.

I just drafted a SS who is projected to have 90+ fielding ratings. My question is that if fielding coaches don't come into play until ML, is my training budget the only factor in his progression?

FI affects ALL levels.   That's why it's the most important coaching position.