1. I get notified for each transaction that occurs.
2. I get a transaction history to review what goes in and out of my wallet.
Does a smart wallet with these kinds of features exist?
Did you ever use ... Electrum? At least the desktop version does all this:
* it shows a balloon notification (on my Win10) if a transaction is sent
* the main view shows all the transactions
So what are you talking about?
To be fair, Electrum only show notification if open the application and wallet. But pretty much most Bitcoin wallet have such feature.