After seeing these questions I'm thinkin' you should pack it up and send it back to Dell ... you're not ready yet.
Why not? These aren't unreasonable questions, at all.
"Can I literally use it on my lap?"
If you're a male, that might not be the healthiest thing for your bait & tackle - at the very least, heat reduces sperm count.
"I heard the bottom gets hot? Does it get so hot that it can discolor my furniture?"
Not a bad question. It can get hot, but I haven't seen mine (a 2.2 GHz Santa Rosa Core2Duo) discolor anything. Then again, I don't have fancy furniture. Maybe something else with a more sensitive finish might get damaged, but I doubt it.
"When I'm not using it for business, I'll have it connected to my tv. Can I just leave it plugged in with no adverse effect, or am I supposed to unplug it when not in use."
The biggest risk is that any surge that hits your TV will also hit your computer. Surges can come in to TVs through an the antenna, cable, or power outlets. People tend to surge-suppress TVs far less than computer power outlets - so your risks, while low, are still higher than if it was unplugged.
"(Seems like Dell would ship some kind of owner's manual with it, doesn't it?)"
It probably has a manual on the disk. I'd mention that my MacBook Pro came with a manual, but that'd be obnoxious.... ;^)
I can always count on FR’s token prick to make an appearance on one of these threads. I guess you’re it.