1. It has to be done in a single day, next day after server safe the points counter resets.
2. You can open the third staga in exactly the same way as second one. All you need to do is to make 200 points during one day.
Note, that you can not make 400 points and jump from 1st to the 3rd stage, so fully opening Hive takes a least two days in a row.
3. Third stage lasts 5 days. When its finished and are back to the 2nd stage, you can make 200 points to open it again. If you won't make any points during 5 days, it will be back to 1st stage.