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 partly answered by L_Church:
(even though not completely correct, since you are not allowed to "stack" a draw card — instead of drawing 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, instead the next player must draw 4 cards from the pile.
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 for that player to DRAW 4 cards from the pile and then it's the next player's turn (who then can play another +4 card or any other card).
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.
No. Unless it's a 2 player game, then you can do it, since it's your turn again (but your opponent still must draw 4 cards).
If it's a 2 player game or only 2 players left, then if you play a Wild Draw 4 / Draw 2 / Reverse / Skip Card it's okay to play another card immediately after you played the first card - since it's actually 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.
1. Playing a Reverse card works like playing a Skip card. By playing the Reverse card, you may immediately play another card.
2. By playing a Skip card, you may immediately play another card.
3. 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.