Some UNO rules questions

Question

I just have some questions about the rules of UNO, since me and my cousins are relatively new to it.

1. Assuming we're only 2 players left, and I already placed my last card (Example, a +4 Card), but then my opponent also played a +4 on top of my +4 card, is it invalid? Or do I get to draw 8 cards?

2. When I play a +4 card, can I immediately place another card on it? (Example, I played a +4, then called out YELLOW, then placed a yellow "5" on top of the +4 without shifting my turn)

3. Also the same question as #2, but if I get to place a "Skip/Stop" card on top of my +4, will that pass the +4 effect to the next player? (Example, I placed a +4 then a skip on top of it. The +4 is dedicated to Player B. By putting a stop, the +4 gets passed to Player C instead.)

Answer 1

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):

1. 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.

2. 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.

   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.

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

Answer 2

1. A players hand must be empty to win a round. Since you've emptied your hand before your opponent you would win the round. Their play would be invalid since the round is over.

2. Playing a +draw card counts as having you play a normal card. In a 2 player game this will just result in having your turn again anyway. In a 4 player game you cannot play 2 cards like this in one turn. It would move to the next players turn in which they will have to draw or chain a +draw card

3. Same as #2, you cannot play 2 cards in one turn