Should virus/malware protection be added to iPhone?

No. There are no viruses in either macOS or iOS. There's nothing to find. All AV software is useless, particularly in an iPhone or iPad. Being a sandboxed OS, the only place such software could even look for malware would be within itself.

That is a very common scam that you will see on any device and under any OS. There is no software in the world that can see what's on a remote computer through a web browser. Simply close any such web page or popup. Similarly, delete any message or email making any such claim.