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Hi, I'm not a ptam expert, but I will try to answer you. The ptam authors will give you better information.
1) Why do you need the grid on the same axis? You will still get localization information with respect to this axis.
2) Make sure you always have translation and no rotational camera motion when you initialize the map. This affects the map initialization.
3) The algorithm looks for change in position of the features when the map is initialized. If there are features at different heights, it means that you are not facing a averagely plain ground plane. This would naturally make the ptam to initialize the grid plane in an inclined manner.
If you find better answers or more information on the same, kindly update this post.
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