For apps you purchase, If you are using the same Live ID on the new phone as the old one you can just download the app. When you select "purchase" the phone displays some message along the lines of :
You have already purchased this application. Would you like to install
As far as your license goes, things like that can not be transferred between devices. What you can do is. a) Install the app, and try entering the same information again. If that doesn't work you will need to b) contact the developer of the applications and let them know you switched phones and need a license for the new one.
Hopefully the company has great customer service and the will work with you.