Can you have WhatsApp on your laptop without having it on your mobile phone?

So that you can just write there

No. At least the version of WhatsApp Desktop that I know needs a smartphone with WhatsApp within reach.

No, of course not, you need a cell phone number that the contacts can reach.

I had the problem that I could only have my WhatsApp app on one device, so I guess it works.

You have to search google whatsapp web

you have to scan the cross code with your mobile phone

then everything goes by itself

If your laptop has a SIM card slot, you could run WhatsApp via bluestacks (android emulator), but whether it works at all and is stable is unfortunately a different matter.