Any Red Dragon?

For the final training step does it have to be the Raid Boss Red Dragon only or can the (easier) Shadow Mission Red Dragons count as well?

Raid Boss, Summoning Urn (for those that hoard...I KNOW YOU'RE OUT THERE), Generation 8's Crumena, and the Shadow Realm Red Dragon will all count towards this. Keep in mind that if you are the lead in G8 Finale, you will be kicked out of the room. Make sure that you make the most hits during the G8 Finale if it is yours.

So the lead of G8 final cannot get the finish on the boss?

Nope. The lead is kicked from Renes and teleported back to Calida Exploration Camp as soon as the dragon's HP hits zero, regardless of who dealt the last blow before finishing it. Everyone else has to leave via the doorway in Renes.

Yes they can get the finish, they just have to satisfy the finishing requirements, or you can simply solo it. Just don't set the finish to Anyone in the Party.