It is a lot easier to give you helpful answers that are specific to your situation if you share the actual automation instead of just a brief description.
There is… In the Calendar dashboard you create an event by pressing the “Add Event” button. Fill in the summary, description, start/end times. Then at the bottom of the popup window you click on the “Repeat” drop-down menu. Select “Weekly”, then type a “2” into the “Repeat Interval” input field and select the day(s) you wish the events to be repeated.
Please post the data from the calendar entity from the Developer Tools > States tool.
Yes, as long as you have a calendar integration that allows Home Assistant to manage it directly using services. Examples of those include Local Calendar, Google Calendar, Caldav, and others.
If this is a read-only calendar from a third party, you will need to add a calendar that you own to be able to add events.