He can replace them, basically use the same funding address, use a higher fee and send the coins somewhere else, so your tractions will become invalid as they have no more source money, to keep it as simple as possible.

Of course you could do the same to prevent this, spend the not confirmed funds , send them to another address by paying fee high enough that will also confirm you current ones, it's called Child pays for Parent and the same is pretty much self explanatory.
https://bitcoinelectrum.com/how-to-do-a-manual-child-pays-for-parent-transaction/

Again, without known the fee, the size, if your in total control of your wallet, a few more details nobody can guide you to the best course of action.
For example if the tx are small enough (in bytes size) and have paid over 10sat/b you could accelerate by yourself with viabtc:
https://www.viabtc.com/tools/txaccelerator