Regarding first issue, when you insert a graph item using the wizard initially your axis scale will be category scale. This means the months will be interpreted as strings. If you try to sort those strings, they will be sorted alphabetically.
To change the internal interpretation of the months you need to use a DateTime scale: How to: Change the Axis Scale
. Then the sorting will be done in calendar order.
Regarding the second issue, you can add a calculated field in your data source replacing empty values with 0: Calculated Fields