(Almost forgot to answer before I went to sleep but I need these internet points)
Yes, the Pokemon you select for a Tera Raid battle will be healed with PP restored as well.
From what I tested, exiting the tera raid by losing, winning, or quitting even if you used moves or have taken damage also seems to heal you. I don't know if this is because I beat the base game but I doubt it.
Source: Experience with knowing going into the raid heals you and testing for the other parts.
Hope this helps.