Yes, you could run MCE on a laptop. In fact Dell sell high-end laptops with MCE preinstalled.
Are you sure you need MCE though? You can do most of what you describe with just XP.
You will struggle to find a new computer without XP preinstalled on it, but you can buy MCE separately from some suppliers. Thread on it
here.
You shouldn't need to install PowerDVD on MCE. Just get a codec (there are a few free ones around) and play the DVDs in the MCE application.
The MCE keyboard and remote use an infra-red connection. The IR receiver comes with the remote, and it's a bit big and ugly, but works great.