Ok, I read the post from top to bottom. This is what I understood:
You do not see calendar periods in Control Payables Periods.
First of all I want to see if your responsibility is connected to the right operating unit. 1- Can you verify the value of MO:Operating Unit profile option for the responsibility you are using. Also verify that MO:Security Profile is blank. 2- Now open up the Operating Unit screen from Accounting Setups workbench in GL (First query the ledger and then go to Operating Unit options). Verify the name of the ledger your operating unit is attached to.
To me it looks like you responsibility is not connected to the operating unit.