Expect the whole process to take ~1 year before you can have plantlets ready to be deflasked so don't be too eager to do stuff
Plantlets are happier the less you mess with them, so err towards needing a reason to change before you do anything. Much like caring for adult orchids if you think about it...
Question 1: If they're happy, agar isn't dried out or phenolic, & plantlets can easily fit out of the neck of your jar, leave 'em be, especially if only 21 days. If you're looking to multiply in vitro, that has some timings you should look up/read about, otherwise, let em stay in P688 and see how many spontaneous shoots you get, and when it looks dry or the plant size is getting large, put them in new media. If you were to transfer immediately into P668, you wouldn't get roots and suddenly a ready-to-go plantlet. p793 is about nutritionally equivalent to P668, P793 just also has some hormones that encourage certain meristem activity. So it's not holding your plantlets back, certainly not after 21 days. Assuming the P793 is prepared correctly.
Question 2: I usually don't worry about removing the stem unless dividing as described earlier in this thread or the stem introduces problematic geometry.
Question 3: Kind of (not the stem, the stem is old, differentiated tissue, but if you leave callous or meristem on there, that can do stuff). Depends on your goals. See earlier posts in this thread talking about this, or let me know if they weren't specific enough and I can point you to some google scholar search terms, etc or else provide some clarification.