I know you can create your own coins in ethereum but can they be used in 3rd party contracts that normally use ether?
Yes, if the 3rd party contracts are set up to use it. If your token follows the token API, then the third party contract should just be able to receive and spend other tokens as long as they know the address of the contract managing the token they want to accept.
Yes but :
Your coin contract methods would have to be integrated in the said contract 3rd party contract ( to have that contract call Send/receive coin methods )
that contract would need to have ether to be able to make transactions as an regular user would.
the coin contract should be included inside the 3rd party contract ( before ) when compiling it so that it can use it's functions/methods.
When you've done that your contract can effectively act as any other use would and use the coins contract methods.