I can only respond for NJ...
1. Yes but it depends on the aircraft -- some are allowed, some are not.
2. Both 1000' and 500' calls are above TDZE and setup as a challenge/response to verify the aircraft complies with stabilized approach criteria. (1000' for instrument approaches, 500' for visual approaches) - The Pilot Monitoring makes the call, and the Pilot Flying responds with "Stable" if the aircraft meets the criteria or executes a missed approach if it does not.
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