Hi!
Welcome - I'm glad you like the app!
The best way to make markings on the battle map is to add effects, which have different shapes and can have any color/transparency.
Adding a general drawing function would be a fairly high effort, but being able to add icons with graphics should be quite easy and is on the roadmap. For the further in the future, these could even be animated. Good idea! There is also a roadmap plan to add DM-only markers to a map which could be also linked to encounters.
Individual character icons are only visible on the battle map, which is the tactical map view. If you want to follow the icons through a dungeon in detail, you can start a battle without monsters with the dungeon as a map, remove the fog of war as they move along and add monsters if and when they appear. You can show zoomed in parts of the map in the Players View, so it doesn't have to get larger as they explore further.
You're welcome to also stop by our Discord to discuss further features!