Yes, however the visa fees for H1B will be forfeited.
Yes, you can fill out new DS160 with the updated information of the new I-797 for H1B, call VFS and provide the new DS160 number so they will update the appointment.
Make sure you carry the old and new DS160 to your appointment.
No need for new appointment unless you want to save the H1b visa fees which will be valid till 30th September 2023.
Call VFS in case you need more help with your appointment.