The Coinomi mobile wallet now has Monero integration. When making a transaction, does the wallet send the private view key to Coinomi servers to perform the transaction?
Coinomi monero dev here!
The server maintains a copy of the private view key to scan the chain on behalf of the wallet. However, this view key is not stored persistently, it is only kept in memory. The server only stores the hash of the address/private view key and uses that for maintaining the account inputs and outputs. This works exactly the same way as MyMonero/openmonero.
Creating and signing a transaction happens strictly on the wallet, except for the output selection part that is done using monerod.
Given this is a "lightweight" wallet, with a closed-source server, I can say with some degree of certainty they have your private view key on their server (whether stored there or sent between client and server when making transactions or updating the wallet's balance).