In your fullscreen panel you seem to try and achieve the carousel to be full with and height of the panel. You can easily achieve this by using a layout: 'fit' instead of using a vbox and setting flex. In the next release Carousel will extend Panel meaning that you could even skip the whole wrapping panel and just make the carousel fullscreen: true.
Also you seem to be using html and items at the same time on your FormPanel. Although this does work, you have to manage the positioning of the html yourself. A better option would be to add an xtype: 'component' as a child of the FormPanel and use the html configuration option on that component. That way you can let the framework lay out the component with html and your form items.
I see you are using layout 'card' on your FormPanel. A CardLayout will make it so that only one item is visible at a time in the container. In your example you will probably want to use something like 'vbox' or even no layout at all.
Finally I think it would be useful to put the form items inside a FieldSet so that they get better styling.