I have an HP dv8000.
You *can* hook up to an external monitor, but I (personally) find it easier to *not* and just use my laptop's screen.
I leave mine on all the time, except when rebooting. Haven't had any heating issues.
This is my *own* and *only* computer... I use it at home and take it with me. I do, occasionally, use an external mouse, but the laptop's keyboard works great for me
But with some laptops, you can get a docking station that hooks to the keyboard, mouse & monitor, so you just insert your laptop and have - essentially - a desktop.