Some UNO rules questions
Here's a great place to read the rules yourself:
From mattel.com: https://service.mattel.com/instruction_sheets/42001pr.pdf

Now to your questions which has been answered by L_Church, even though not completely correct
(you are not allowed to "chain" a draw card - instead of drawing the cards from the pile yourself):


Yes it's invalid, it's not allowed by the next player (opponent) to play +4 card on top of a +4 card.  

If you have played your last card you have won, no matter what happens next.

But even if that wasn't true, it's not valid to play a +4 card on top of a +4 card, 
instead it's MANDATORY to DRAW 4 cards from the pile and then it's the next player's turn who then can play another +4 card if wanted.

Anything else is just house rules...


  Wild Draw 4 Card - This card allows you to call the next color played and REQUIRES the next player to pick 4 cards from the DRAW pile and FORFEIT his/her turn.

Yes, in a 2 player game, but not in a game with 3 or more players.

If you play a Wild Draw 4 / Draw 2 / Reverse / Skip Card or and you are only 2 players, then it's okej to play another card immediately after you played the first card - since it's your turn again.

If you are more than 2 players, then you are not allowed to play another card - since it's not your turn.


  Rules for Two Players - The following special rules apply to two-player UNO.  
  
  
  Playing a Reverse card works like playing a Skip card. By playing the Reverse card, you may immediately play another card.  
  By playing a Skip card, you may immediately play another card.  
  After playing a Draw 2 card or a Wild Draw 4 card, your opponent draws the number of cards indicated, and play is back to you.
  

No, you are not allowed to play 2 card in the same turn.