Does the MB Air with thunderbolt only connect with Apples Thunderbolt monitor? What are the options for third party monitors with DVI or VGA?
They're the same as for other computers with Thunderbolt:
You can use any Mini DisplayPort adapter that you might already have, or any that are available for purchase. I have my brand-new 2011 MBA hooked up with a Monoprice MDP->DVI adapter right now.
The MB Air has a Thunderbolt port but you can also just plug in a Mini DisplayPort with an adapter to a pretty much any monitor or TV you want. You can use a number of adapters such as Mini DisplayPort -> DVI or HDMI.
Mini DisplayPort to DVI on Monoprice
Mini DisplayPort to DVI on Apple Store