Hello Max,
Thank you for your detailed inquiry. It help us easier understand your situation.
Talking about late records, there might be the reason that "Min Period" and "Send Period" parameters on "Data Acquisition" settings have different values than 1. If you want to get data from the device every second, you need to set the mentioned parameters value as 1. As an example, please check the picture below:
Talking about GPS accuracy when a vehicle is parked, could you please provide us a screenshot like the example below?
Looking forward to your answer.
Best regards,
Teltonika Support