I am not a CA attorney. However, as a general proposition, a party can be made to appear in state court proceedings (including depositions) regardless of where they presently live. You may wish to schedule your deposition for before you move out of state. There are alternatives to a personal appearance - such as telephonic and video depositions.
I am not a CA attorney, laws vary from state to state, therefore you should always consult a local attorney.
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See Code of Civil Procedure Section 2025.250 - deposition needs to be within 150 miles of your residence. If a deposition notice is served prior to relocating to the East Coast, you will probably be required to attend deposition in California since it is valid at time of service. Also, additional interrogatories after the intial set are permissible; a party can serve multiple sets of interrogatories.
Everything you describe is proper. As for the deposition, you could be compelled to come back to California.
You might be able to work with the attorney to arrange a video-conference deposition. But if you can't work it out, he will get an order compelling you to appear.
If you have legitimate reasons for not appearing for a deposition, then you can file a motion for protective order. I don't know if you have any reason that would qualify for a protective order.
Contact a local civil attorney for a consultation - a real estate attorney would be best.
As long as neither the numerical limit nor the time restrictions on interrogatories have been passed, the new attorney may file additional interrogatories. Whether you can be deposed in California will depend on when you received the notice of deposition. If a deposition notice is served prior to relocating to the East Coast, you will probably be required to attend deposition in California since it is valid at time of service.