I am famous for not reading things pertaining to something new until well after all the hoopla is over.

I just clicked on my buddy list to see if I had the games moderator on it, because I am in 3 swaps that have/are going to end. All I see is boxes next to each name to either accept the invitation or decline. There are some invitations I don't want to accept as I don't know who these people are, but how do I know who I have actually accepted? I vaguely remember some invites early last week, but it was very early in the morning, and I can't remember who I accepted!!!

It said something about I would see my buddy list when the conversion is done?

I hope I'm understanding your question correctly, but if you've already accepted people, then they should already be on your buddy list.  You would not get another request from those folks. 

Yes, you'll have to decide which members on your old buddy list you want to send invitations to and which to delete. After they are all taken care of you will see your new buddy list.