Several date math questions

All dates are indexed as a long field with a value which is the epoch time in milliseconds, so effectively the dates are converted to UTC.

If you have enough memory to load the date field into the field data cache then you could use the 'field_data fields' feature to see the indexed value, but I would only advise using that as a debugging option here and not as your final solution.

Would the following work instead?

"range": {
   "timestamp" : {
       “gte”: “now/w-1d”,
        "lt": "(now+1w)/w - 1d"
   }
}

This should find the beginning of the current week for the start of the range and the beginning of the next week for the end of the range.

As far as I know there isn't an offset for range queries since you have complete control over the start and end of the range. In the date_histogram aggregation the offset parameter is used to adjust where the buckets start from but this doesn't really apply when using a single filter.

I don't think there is, sorry.