Laying my imac on its side - can I

You can, if you really need to. It's not as though it traveled all the way from the other side of the globe upright all the time.

If you lie it on face-down, I'd suggest putting a towel or other soft cloth underneath it so it doesn't scratch the screen. Don't use anything thick that would be smaller than the entire size of the screen or it risks putting pressure on the screen which could damage it.

Regards.

I would change the furniture or move the iMac elsewhere. What you are proposing is an accident waiting to happen!!!!!!!!!!!!!!!!!!!!

The only issue I can imagine is with the cable connections that may be moved too much and putting stress on the ports leading to a loose plug.

Well I think your decision may be short sighted as accidents can occur any time, but good luck.