This one's easy.
Yes, they are both members of the Star Alliance. So, for being gold on USAirways, you are automatically "Star Gold," across the entire Star Alliance network. The benefit of first class upgrades (unfortunately) is NOT one that you will be able to get when flying on Continental. That being said, most other benefits are reciprocal. For example, priority boarding? Yup! Lounge access (when flying internationally)? Yup! Free checked bag with a higher weight limit? Yup!
The next question is about miles. Because they are both in the Star Alliance, you can redeem your USAirways miles for flights on Continental, or any of the other 26+ partners they have. Same goes for anyone with Continental miles - they could redeem for flights on USAirways or any of the other 26+ partners as well. So, the key is to not have a few thousand with CO and a few thousand with US. If you're flying on Continental OR USAirways, make sure you earn miles on USAirways. It will not only help you keep your elite status, but will help you earn miles to later use on partner flights.
Be careful though... Not all flights will earn 100% of the miles you actually fly. For a full list of which "fares" will earn you miles, check out THIS LINK. It shows which Continental flights you will be able to earn USAirways miles on.
For US' other partners, THIS is the link you want to check to ensure you can earn miles. It will show you ALL of their airline partners and which flights you can earn miles on.
HOPE THIS HELPS!