There is no time limit. As soon as you get an H-1.
She can. For Indian citizens, H-1 and L-1 are two obvious choices.
If you travel during change of status, the request for COS is deemed to be abandoned.
You will be exempt from the quota (assuming your previous employer was a private employer - NOT exempt from quota). The new employer will need to apply for an H-1 again.
Once 6 years on H-1 are over, I know of only two ways to reactivate: go physically outside USA for one year, OR apply for a green card, one year after which you can extend your H-1 (or upon approval of I-140, whichever is earlier).
I am not sure what you mean by "cost," but I can refer you to what we charge. See if this answers your question: http://www.immigration.com/services-fees/h-visa/h-visa-services-and-fees
Some questions from the community:
a. If I want to get my F-1 stamped from India, do I need to submit I-539 form also to the ISO of my school ?
No. An I-539 is used if you want to change status within USA.