You can use FF7.exe with R05C and 7ThHeaven, but stick with only with Textures/Backgrounds Mods, otherwise things might not work correctly.
Mexico hard mod won't probably work. ( didn't try! )
HD menu is only available on previous R04e version ( provided also by 7ThHeaven in Reunion mod ), won't work in R05C.
The new reunion will probably be updated in new 7ThHeaven mods, but some features might not be possible, check Catalog / Mod Requests.
Regarding the music, I am not sure what you mean, but 7ThHeaven provides a Music Mod (has more options and fan made music), it's optional as all mods.
Button Mapping? No idea, I set the mapping, save the game and that takes like 20 seconds. Check PSX/PC Mapping Here:
OK ○ Numpad Enter
CANCEL × Numpad 0/Insert
SWITCH □ Numpad ./Del
MENU △ Numpad +
PAGEUP L1 Numpad 9/PageUp
PAGEDOWN R1 Numpad 3/PageDown
CAMERA L2 Numpad 7/Home
TARGET R2 Numpad 1/End
ASSIST SELECT Numpad 5
START START Numpad -
R05C + 7ThHeaven Setup:
1. Convert the game using 7th Converter.
2. Remove/Hide ff7_en.exe (Steam executable) from the folder and install R05 (otherwise R05C will install on Steam Version).
3. Merge the Texture Folders (Reunion / Textures in mods path) (Optional?)
4. Apply 7th Heaven mods (I usually just apply Textures for Models and Backgrounds) and have fun playing
Hope this helps...