Hey there @Teodora68377 - excellent questions! 

I have great news, as well! Calendly automatically adjusts for daylight savings. When invitees book events before or after daylight savings, Calendly adjusts the times they see so events are scheduled at the right time. You will see the correct time based on your time zone + daylight savings that takes place in it, and invitees will see the correct time for their time zone(s) + daylight savings that takes place in them. (If nobody has joined a call after it was supposed to start, there’s a possibility they forgot, they didn’t pay attention to their calendar or any other number of things.)

As a general overview: 

How Calendly handles invitees' time zones

Calendly will automatically detect your invitee's time zone and adjust the display of your availability accordingly. After scheduling with you, the event added to their calendar will reflect the time zone from their calendar's settings.

If an invitee would like to view your availability in a different time zone, they can expand the drop-down menu on your scheduling page and adjust the display setting.

How Calendly detects your time zone

Calendly automatically detects your time zone when you create an account. When an invitee schedules an event with you, it is published to your calendar in the time zone you've set within your calendar settings. You can view or change your time zone at any time from your Account Settings.

I hope this is helpful. Have a great day!