Warcraft Logs and Raid Markers

Is there a way to see who casts them? I’d like to debug some assists’ addons.

Nope, not in logs.

Can we see on the site when the marks are being set (outside the replay? I noticed that you do set marks on players and npcs correctly (on the replay). That means the application information does exist somehow (in the log).

The events view shows it as well. You can write an expression to filter to events with raid markers, etc.