1) Are you sure that's not just the screensaver or power saving option configuration (I'm not quite experienced with Vista Basic)?
It could be that the PC falls in "Sleep" mode which is a really good thing I use all the time (It beats shutting down your PC). You just need to do something like tap one of the arrow keys on your keyboard to resume from Sleep and get back to the Welcome screen.
If your PC has been in Sleep mode for a very long time, it may go into Hibernate mode which saves whatever your doing to the Hard Drive and then shut's down your PC. In this case you'll obviously need to press the Power button to turn your PC back on.
Hope this helps somehow.
2) I really don't know. Just guessing: TinyURL is probably powered by a database. You submit a lengthy link in a form. In turn (magically) there'll be some code that gives a shorter random link based on whatever shorter links hasn't been used yet.
Overall I'm guessing it's just a lookup/page redirect function. You enter the tiny url, it looks up the real link in the database and page redirect's you.
With a little imagination I'm pretty sure you could come up with the same thing.
I hope this helps/leads you somewhere.