I heard from my local computer shop, that if you connect two inputs into a monitor and use them at same time, it would damage the monitor. Is this true?
It depends on the monitor, if it has multiple data connections (e.g. one HDMI and one DP) you can physically connect both of the at the same time. But with most (cheap) monitors you will have to switch between them. Displaying both input sources on one monitor is only possible if it supports the feature (e.g. via the PIP feature) usually a bit more expensive.
There are also third party adapters that allow multiple devices to connect to the same connector e.g. KVM switch. Most of them only allow for switch between the sources not displaying both sources at the same time.