Can Facebook live be done with desktops and laptops ? If no will it be made available soon ?

I'm starting to learn what I can about Facebook live and I know it's designed to work with mobile phones and hopefully tablets too.

Me and my family have and operate several FB pages cause we have businesses. So a few questions come to mind as I research FB Live:

Can it be used with Desktops and laptops? Many laptops come with built in cameras and desktop people can buy webcams

Would it work with a camera(Camcorder or DSLR) connected to a phone, tablet, or laptop?

I've heard FB Live works for pages but where is the Live option/button?

I've also heard the videos afterwards are saved in your videos tab; will they be downloadable ?