OK, let's look at the Login module first. This is what I did on my test site. In the Joomla back (admin) end I went to Module Manager. I selected the Login module with a tick in the left hand box and clicked the copy icon next to the words Module Manager. This gave me a new module called "copy of login" which was not enabled. I then clicked on the module name "copy of login" and it opened the editor. I then changed the title to "Iphone Login" so I would know what it was. I changed show title to (no), enabled to (yes). Next to the word position is a drop down menu, I selected mj_iphone_middle. Just for this test, make menu assignment, menus (all). Then save. Then load the website in iBBDemo2 and you should see the login screen. You may have to click on the screen and then use the down arrow to scroll the screen so you can see the login part.
The mobile templates do not have all the places (positions) that are in the normal site template. That is one of the features of Joomla, that a template can be designed with specific locations (positions). There are 4 mobile joomla templates, one for each class (type) of mobile browser. The positions on the mobile joomla templates start with mj_ you can experiment to see where they are. Let me know if this works on your site.