Follow the code for createrawtransaction. If you are interested in how the wallet works, then follow the code for sendtoaddress

Yes. However the checking and adding to mempool are done as part of the same function. The AddToMemoryPool function will call the various checking functions for checking a transaction and then add it to the mempool at the end. It also performs its own checks for the additional conditions of adding a transaction to the mempool (e.g. conflicts, replacement, transaction fee, etc.).