The channel is 7/8" tall. Different clips with have different dimensions, but I believe that the clips and channel system will lower the ceiling by about 1.5"-1.75".
You can also do something like this to save a little headroom.
Clips cannot be used without channel. You need both.
24" on center stud walls will allow some more flex and are preferred. Check your local building codes though. I believe that is is ok as long as they aren't load bearing.
They sell batt insulation that is made to be installed with 24" on center spacing.
Yes, insulate the ceiling with fiberglass batts too. Faced or unfaced doesn't matter much in this case, but the faced stuff allows you to staple it in place fairly easily.
A few more things;
1. I hope that you are treating the walls of the room as well. (decoupled, double drywall, green glue)
2. All of those can lights will need some sort of backer box to surround them and keep any sound from escaping through the hole that they make in your soundproof shell. Also, your electrician will likely want to rigidly connect them to the joists. This will recouple your ceiling to the house structure. You should be looking at fixtures that are "clipped" onto the drywall. Many are labeled as "old work" or "remodel" fixtures.
3. What about all the other penetrations (outlets, switches, HVAC)? Do you have a plan to address those as well?