First question - Who is the best person to ping to request a thread be moved between forums? Is it the mod of the forum it is in, the mod of the forum it is going to, or someone else? Second question - Is it possible to move threads from the main forums into forum groups? Is the person you request to do that different than above?
I have an answer to the first question, it's the MiniMod in the Forum where the post currently is. If it is outside of any of the Forums that they are the MiniMod for (some MMs do more than one) they cannot touch it.
My response to the second is a guess. Forum Groups do occur in a different forum/subforums from other posts so you would have to move it to the forum/subforum which has your FG using the MiniMod of the original location. and then once it is transferred to the forum/subforum where your FG is the MiniMod of the new location would be able to move it within.
I do not sorry. You may have to ask via Ticket in Help, the mod here might know who to ask, or occasionally some other user or staff will pop by and know the answer hopefully.
There are no minimods assigned to the event forum, so you will have to file a ticket so that any staff who are online can move or lock your thread for you :) This is because the event forum isn't always here, I think, so we don't get assigned to it.
As for the second question, yes, you would probably be able to get a thread moved from main forums to a forum group, but I would also file a ticket to ask for that to be done just cos it's a bit more complicated on the back end ^^ :)