All Heal over Time (HoT) effects stack with all other HoT effects from other healers. For example: WHM 1 casts Regen on the main tank and Medica II. WHM 2 also casts Regen on the main tank and Medica II. The main tank will have 2 separate Regens and 2 separate Medica II actively healing. So that's a total of 4 HoTs going at once. This includes all AST HoTs while in diurnal sect.

All shields from SCH and AST (nocturnal sect) overwrite all other shields from other SCH and AST. Example: SCH 1 casts Succor on the party. SCH 2 then casts Galvanize on the main tank. The Succor shield would be overwritten by the Galvanize shield.

As for buffs? This is mostly referring to Card buffs from AST. All card buffs will replace any preexisting card buff. Protect also doesn't stack, so only one person needs to cast it. Same with Stoneskin.

The basic rule is: HoTs stack, everything else doesn't. Though, there are a few exceptions (Eye for an Eye stacks iirc).