Is it possible to check with the mempool if a transaction is being sent to one of my addresses and send me a notification sms or mail?
With Electrum? Impossible, but there are some services which automatically send email / SMS when an address have new transaction.
Blockchain.info (now blockchain.com) used to have such feature & you can use it on watch-only wallet, but i don't know if such feature is still exist.
Second question, if one of those addresses are receiving a transaction can i make a script that will auto transfer the amount with a custom fee depending on the actual fee price so that I can balance the speed/price without over paying the transaction cost and not wait too long
It might be possible, but i don't know whether Electrum have feature to execute specific script when there's new transaction (which is required to achieve task)
WTF, maybe, but dont know, it might be possible, but i dont know, why are you even bothering answer this request while all you do is write maybe or I dont know?