@Rajiv3
All good questions - it's good that you're conscious of this as many hosts do not give it much thought.
1) No, no permit is currently needed to operate your Airbnb in Houston (or Harris County).
2) Besides the occupancy tax that Airbnb collects from Texas hosts (and pays on your behalf), there are no other local taxes that you need to pay.
With that being said, just be sure to claim your income on your yearly taxes. Airbnb has published a wonderful 40+ page document (after hiring consultant on the subject) that directly addresses Federal Income Tax and how Airbnb hosts are affected. Not sure where it is but do some searching and I'm sure you'll run across it.
Mark the Host