Monopoly Deal - property wild card queries
In answer to the first part of your question: we have always played that you can't move a card from a stack with a house/hotel expect to pay another player. However, I can't seem to find a rule written down that says this. 

For the second part of the question: my initial assumption was that you can't do this. However, the rules say you can rearrange your cards in any way you choose during your turn. It is worth reading the section below from monopolydealrules.com who are usually very good and as close to an official rules site as the game has:


  Can a House or Hotel card be on the table without being apart of a full/completed set?
  
  Yes, but you cannot lay down a House or Hotel card unless you can play
  it on a completed set. However, if a player charges you money and you
  decide to pay with some of the property from your completed set that
  includes a House and/or Hotel, the House or Hotel must be placed on
  the table next to your property section until you complete another set
  and it can be placed on top. You can also pay with your house or hotel
  card if you choose.


I hope this answer helps and if anyone has a better answer I'd be very happy to be corrected!