You can create a new category either by navigating to the "Add Categories" page through clicking the chevron next to the add button and clicking on "Add Categories", alternatively you can add a new category through a new task by clicking the add button next to the category choice. From there, you can enter a name and choose a colour for your new category.

Yes, to do this click the edit button on the home page and tap on the task button, this will change to categories view where you can find all your categories and can edit them by tapping on the wanted category.

You can view your statistics by tapping on the "Stats" tab. This will show you a breakdown of your time spent by category, if you want more detail for a specific category you can tap on that category and get a breakdown of the individual tasks for that category, as well as your progress over time in the form of a graph.