Is it possible that if my employee sends another transaction with higher fee to my address (which you probably directed), will it reach faster? I'm waiting for the confirmation so that I can start working. But if there's any way of cheating, I would ask him to send again.
If the transaction has the RBF-flag set (Replace-by-Fee), then yes. He could simply bump the fee.
If the flag is not set, you either have to do a CPFP or ask him to send another transaction.
But sending another transaction is not recommended because both may confirm ending up in you receiving the double amount.
So the best (and fairest) options are either a RBF by the sender or a CPFP by you.
And yes, he still can cheat you until it is confirmed.
If the RBF flag is set, he can replace the transaction with another one sending the funds to a completely different address.
That would be even possible without the flag set, even tho being not that easy to achieve.
If possible to send with higher fee, what will happen to the current transaction? Will it remain unconfirmed forever?
If you are refering to bumping the fee (i.e. RBF), nothing will happen.
The bumped transaction will confirm and the old one will never be able to be included into a block.