I think you are on the right track. The output of:
forEach(value.parseJson().calendar_months, e, e.days)
is hard to read because OpenRefine and JSON both use square brackets to indicate arrays. What you are getting from this expression is an OR array containing twelve items (one for each month of the year). The items in the OR array are JSON - each one an array of days in the month.
To keep the steps manageable I'd suggest tackling it like this:
First use
forEach(value.parseJson().calendar_months,m,m.days).join("|")
You have to use 'join' because OR can't store OR arrays directly in a cell - it has to be a string.
Then use "Edit Cells->Split multi-valued cells" - this will get you 12 rows each containing a JSON expression. Now for each ID you have 12 rows in OR
Then use:
forEach(value.parseJson(),d,d).join("|")
This splits the JSON down into the individual days
Then use "Edit Cells->Split multi-valued cells" again to split the details for each day into its own cell.
Using the JSON from example URL above - this gives me 441 rows for the single ID - each contains the JSON describing the availability & price for a single day.
You've now got some pretty easy JSON in each cell - so you can extract availability using
value.parseJson().available
etc.
Owen