How can I add links to the my custom applications in Manage Group panel?

Are you referring to an app you created that uses IApplicationType?    Dose that type also implement  

Telligent.Evolution.Extensibility.Content.Version2.IManageableApplicationType

IManageableApplicationType provides possibility to Create, Delete and SetEnabled (and Search and List).
I don't see any members to set seomething else.

And yes, I implement IManageableApplicationType

IManageableApplicationType provides possibility to Create, Delete and SetEnabled (and Search and List).
I don't see any members to set seomething else.

And yes, I implement IManageableApplicationType

It has a much more robust interface than those:

IManageableApplicationType (v2) Plugin Type

To add it links are not showing up and you implemented the appropriate method, like Edit->CanEdit  make sure that actually returns true for the user based on whatever logic you have implemented.  Not showing up usually means its returning false or something else is wrong.

Hm, I debugged and see that related to IApplication.Url (should be NOT null).

Will research that next week.

Yes, that also depends on IApplication.Url value - it should be not null.