How to specify the minimum and maximum value in the URL parameter?

It cannot be done directly with the help of a URL parameter. but you can create a calculated field for this any use windows_max function to achieve this. Here you can provide the allowable range with your URL parameter should take while in dashboard action. A quick filter can also accomplish this task.

How to update the month parameter to the current month automatically?

This can be done by applying the filter on the month dimension. drag the month column in the filter shelf and select count.

then on the filter pane check the box to filter the data on the current month. this way you can update the month parameter to the current month automatically.