Does a contract calling a function defined within itself cause an Event to be emitted? Etherscan is not showing events emitted when a function is called using sendSignedTransaction(), despite the fact an Event is within that function.
Yes, if you have defined the event in the function that is being called.
Provided that the event was set up correctly (I can confirm if you add the code to the original post), the EVM will emit each event as they occur.
The Etherscan link you provided is a wallet (as opposed to a contract). Etherscan should pick up all events that occur on the blockchain for a contract, and they will be reflected in the contract's page on Etherscan.