Yes, if you are running Bitcoin Core on the same machine that is live on the internet you are asking for trouble.
I'm the kind of guy which has 1 machine only but still wants to have a full node (pruned) running and using bitcoin core as a hot wallet. Does this mean "I'm asking for trouble"? To what extent?
Generally, you should never need a browser extension to talk to your Bitcoin node, through RPC or anything. Why don't you simply run a client such as c-lightning or LND alongside your node?
Also, can bitcoin core run and work as a hot wallet in a machine that is not connected to the internet?
No, unless you utilize PSBTs, which Core supports well.