Is it within the rules to put a wild draw four card on top of a draw two card, as it is a 'higher' card? We've ALWAYS played that you can, but my new friend is adamant you can't.
A common Uno variant allows the recipient of a draw 2 to avoid drawing (and being skipped) by playing their own draw 2. The next player either needs to skip their turn and draw 4 cards, or play their own draw 2. If they play their own, the next player must either draw 6 cards or continue the sequence. Some variants allow similar behavior with draw 4 cards.
Assuming you're talking about this "stacking" draw cards, you aren't going to be able to get an official answer, because it isn't an official rule. This would explain why you and your friend are both adamant about it working in different ways. You're just going to have to come to an agreement on how you will play.
For what its worth, every place that I've seen this rule described you have to play the exact same card, so you cannot "stack" a draw 4 when receiving a draw 2 in order to make the next player draw 6. So I expect that is the more common way of playing the variant.
You can play a Wild card on top of anything, so long as it's your turn to play. Your friend is crazy.
For the Wild Draw 4, you should ideally be unable to match the color - it is possible to challenge a Wild Draw 4, and if the person who played it could have played a card to match the color instead (not the number), the person who played it has to draw the 4. If the challenge is wrong, the challenger draws 6 instead of 4.
According to this link (http://www.qcsalon.net/en/uno), a +4 can't be played on top of +2 or vice-versa. There are other rules too, regarding playing of a +4 card, you can choose to follow.