The icon that shows up in browser notifications or the start page seems to be the custom icon for my first forum however it's looking very very tiny over a black square - so it doesn't really work. Is there a way to set a specific icon to show up in those places? 

You can set icons in ACP -> Customization -> Appearance -> Icons & Logos.

Thank you! That worked great. 

You're welcome, glad to see your question is resolved. 🙂