How do I re-download songs I purchased on the iPad, after formatting the iPad?
Yes the purchased tab in the app stores should allow you to re-download most if not all of your purchases. If you have previously hidden some purchases, you may need to access your Apple store account (Apple ID) to see the unfiltered list of past purchases.

Please see this link or this link on Apple's website for more details. You can edit your question or ask another if you find a problem on a specific step.