Nick: Sorry for the delay, but I was playing most of the day and not at home.
1. The player did not protect his hand, that said, if this was a new player and inexperienced, I would try to retrieve his "lost" card. To do that he would have to tell me what the missing card was both in terms of value and suit and I would have to find that missing card in the muck. One chance only. If this was an experienced player, sorry, but your hand is dead.
2. Same answer. To have a valid hand the player MUST have two hole cards. Again I would take into consideration the experience of the player etc., as I said above. Remember this player gets "One chance only". This doesn't mean one chance per event. Had that player not protected his hand previously and 'used his one chance', the hand is dead!!
Finally, while I totally understand what you are trying to do (at least I think I understand) with the rather detailed changes you have suggested to different rules, I think it is more than what the TDA is comfortable with. In my opinion, and I am not speaking for the TDA BOD in any way, shape or form, one of the desires of the TDA BOD is to resolve the most difficult and confusing situations with brevity in mind. There is a reason for that part of TDA Rule #1 which says, "...Unusual circumstances can on occasion dictate that decisions in the interest of fairness take priority over the technical rules..."
What is important, in my opinion, is that consistent decisions are made. It is just unacceptable to me that floor persons in the same house will take identical situations and make different rulings. I can accept different rulings from one house to another, but NEVER within the same house.