New iMac

Go to System Preferences (found under the Apple Menu, at the top left of your screen) and open iCloud. Put in your account information there (which should be the same exact Apple ID and password used by your iPhone and iPad). Enable whatever you want synced. It's pretty much automatic at that point, and you will see all of your contacts and calendars on your new iMac.

I do not select that. It is a method for you to control your computer off-site, allowing for screen sharing and file sharing. Do not open this, as it is a security hole (though password protected), unless you have specific reasons.

http://support.apple.com/kb/HT1449

Make sure you enable "Find my Mac" which allows you to track it if someone steals it, though if they wipe the disk, it won't help.

It allows you to share some data between your iMac and your iPad. It works best with iWork (Mac's version of Office, and much better, IMHO). You can save a Pages document (like Word) to iCloud. And if you have Pages on your iPad, you can edit it there. I use it all the time.