Sounds like you need a minor adjustment to fix the speed of the watch. As for the wind down, this does not sound normal. To test, fully wind the watch and let it run down or set it to 12 and do the same thing so you will see exactly when it stops. Anything less than 30 hours should be seen by a service center. Even if you run a chrono, it should not unwind this fast.
Could be nothing, but should be looked at. Omega makes a great watch.