I've figured out how the links should be
https://'your-server-IP'/manager/bil...lected-package'
The project ID always = 1 (project=1) unless the BillManager is corporate version.
The service function can be viewed in Products->Item Types, The function would be the Item Internal Name of the corresponding service.
The package ID can be viewed in Products->Packages, it would be the package ID number.
The Order Period ID can be viewed in the 'order periods' page of a selected package. to access the page select a package in Products->Packages and hit the 'Orders Periods' button.
A link like that one opens up in the Registration box, if you want a link that opens up in the login box you just have to change 'register' for 'logon' like this:
https://'your-server-IP'/manager/bil...lected-package'