I noticed you did not get any response on this. I found that my new smartphone did not show all categories; rather, it only showed categories for categorized items added/synched. To remedy this, I added a task and assigned all GTD categories to it. After this, I found all categories on my smartphone, and deleted the fully-categorized task.
As to viewing tasks by category, it appears one has to install something to enable viewing tasks by category without multiple clicks to filter by category. I am investigating alternatives to help with this, as not having easy access to a filtered task list limits the use of the smartphone as a GTD tool.
Hope this helps you (or someone else)!