If you held a higher grade at some point previously, they can give you a higher step based on your highest previous rate, but otherwise, a reassignment does not increase your pay.
As for the promotion, there's a two step rule. If you are a GS-5 step 2, for example, you would look at the GS-5 step 4 amount, and then give you the lowest GS-7 step that equals or exceeds it. The amount for a promotion to GS-7 varies depending upon your location. If you are in Dallas, TX, for example, a promotion from GS-5 step 2 to GS-7 step 1 would be an additional $6,798. If you are in a Rest of the United States city, it would be $6,431.