Exposing F5 dashboard publicly?

Another related topic would be: is it possible to expose dashboard on other vlan than management? For example as conventional Virtual Sever in some other network with destination pointing to F5 management IP?

If you allow HTTPS in the port lockdown settings of a self-ip, you can access the Configuration utility via that self-IP.

How to expose dashboard without requiring authentication / requiring different authentication than F5 Configuration Utility

There is no mechanism for doing this.

Is there any lower permissions level for account in F5 than Guest that allows dashboard access or can this role permissions be even reduced to access only selected statistics required for dashboard operation?

Guest and Auditor are the only Read-Only user roles. Manual Chapter: User Roles

There is no fine-grained user-role access control for the Configuration utility.

The RestAPI does allow for fine-grained roles control

and you can extract device statistics via iControl

Take a look at Ps Icontrol Dashboard for an example using Powershell