How to determine if there are events in a calendar?
Looking at the docs you can search for events for a certain calander by including the id or the handle in your query.

{% set calendars = craft.calendar.calendars({
    limit: 100,
    order: "name",
    sort: "asc"
}) %}

{% for calendar in calendars %}
    {% set events = craft.calendar.events({
        calendarId: calendar.id
    }) %}

    {% if events|length %}
        // there are events
    {% else %}
        // calendar has no events
    {% endif %}
{% endif %}