It's surprisingly common for people not to own a non-work computer other than a phone/tablet, especially now that prevalence of desktop computers is declining. Some people do still have a home desktop, or a separate personal laptop, but a lot of people I know don't. Or they might have one but it's a shared family computer that's mostly used by the kids, while parents use their work laptops.
This is correct.When all this Corona thing started,we put the entire office on remote. Before we did it,we had to assess who's got what at home. In my department it was about 20% without a laptop/pc. In others was similar.We simply gave company's PC to take home and called it a day. It's a small company, so obviously things are simpler here.
It's something I would strongly recommend against, since it gives your employer easy access to monitor you, and if for some reason your employer winds up in court, everything you used the machine for could end up read into the record.
Eh. Depends on how much control the company has over devices being used for work. I have a number of different computers--including a company-issued laptop that I use as a Linux system. But I mostly use a personal MacBook for both personal and work use. I travel a lot (normally) and really wouldn't want to have to travel with a laptop that was strictly for work use.