Yes, there is a community pool in this development. As well as a game room, fitness center, and club house. There does not appear to be a tennis court. There are common grounds and it is very near Lake Travis and Lake Austin. The amenities as they list them are:
Lagoon Style Pool with Beach Entrance
Fully Equipped Fitness Room
Party Room With Full Kitchen
Covered Patio With Outdoor Fireplace and TV
Unfortunately, the home you are asking about sold in 2011, but there are currently two Ashton Woods inventory homes available, as well as the possibility of still building in this community.
If I can help you find a home here in Austin, by all means feel free to contact me.
My email is firstname.lastname@example.org and my phone number is 512-797-3903. I would love to help!