You mean the skill does not work when using it in the first turn? Can you explain it a bit more detailed I think I don't undertsand whyt you mean?
Sadly that is not possible, since they are not the same skills in the database but slightly modified versions, so the skill levels cant be shared unfortunatly.
Healing potions and skills are affected by the chaarcters healing rate. If Nana has for exsample a 125% Healing Rate all healing potions and skills would do extra 25% healing.
Hope that clarifies it!