Hi Kate!
You can come to Magic Kingdom and stay as long (or as short) as you please :-)
Just remember that they will charge you a full day's admission no matter the length of your stay...
And yes, you certainly can pay for tickets on line, and pick them up when you arrive at the theme park. This is called "Will Call Pickup," which you can pay beforehand, and then pickup at any of the theme park ticket booths before entry. The advantages of this is that the tickets don't get lost before or during your trip, and that you'll save a few bucks in shipping costs. To order tickets online, click here.
In terms of parking: If you will be driving to a theme park, Disney offers ample parking space to its guests. You can park, and then catch a Disney tram, which carries guests very near the theme park entrance. I just need to note: if you're driving, and not staying at a Disney resort, there is a charge to park, which is approximately $14 a day at last check.
Hope this answers your questions. Good luck with all your planning!