I have my wallet set to generate a new receiving address for each transaction. Do the addresses ever "expire"? (i.e. can I save one in another wallet's address book (Electrum) to be able to send back to the Coinomi?)
No. your addresses will never expire and all your addresses will be bind together by a single master public key (xPub key) and is secured by the master private key which is the passphrase shown after opening the app for the first time.
But you cannot import Coinomi's recovery phrase on Electrum. I tried it before but it never worked. Maybe my passphrase was password protected or Electrum couldn't recognize the pattern of the phrase.
Also, when restoring a wallet, what is a "BIP39 passphrase"? Who would/wouldn't want to use it?
BIP-39 is an added layer of security where your passphrase is protected by another password of your choice so that when you import it you will have to enter that password also otherwise it will not import. But this feature is not available on Coinomi yet. They will be adding it in their next update hopefully
Importing standard keys will be available in one of our upcoming versions.
