Actually, that level of ATC is provided by tower controllers in Class B, C, D, E, and Class G airspace.
There is no provision in FAAO 7110.65 for moving VFR aircraft around a MOA. Why would there be? VFR aircraft are permitted to enter MOAs, see
AIM para 3-4-5.c.
In Class A, B, and C airspace, yes. In Class D and E airspace advisories are issued between the jump aircraft and any other traffic, nothing more.
Nope, ATC doesn't move aircraft around Alert Areas. They are depicted on charts just to alert nonparticipating aircraft to high volume pilot training activities.