How does DayBack show conflicts?

The calendar "shows" conflicts, instead of preventing them. So you'll be able to see that two events overlap for a given resource on a given date/time.

Can I show activities side-by-side instead of overlapping?

Yes. In Admin Settings / Views you'll see a setting for "Show events overlapping"; just set that to "No".

Preventing conflicts in Salesforce

You can prevent conflicts using a custom event action in DayBack. You'll find a video and example code here that you can customize to exclude certain events from contributing to conflicts (you might want to accept conflicts with "canceled" events, for example). 

If you want to enforce the prevention of conflicts in the backend, you'd use a trigger in Salesforce. This would alert your users to conflicts they're inadvertently creating even when they're outside of DayBack. Examples and trigger code you can copy into your own org are available in our blog here:  Date Range Conflicts in Salesforce

Prevent double-booking in FileMaker

We’ve created a simple script you can paste into your copy of DayBack Calendar to help notify users when they’re creating a conflict. That script, along with a video and details, can be found here: Prevent Conflicts in FileMaker 19.