Hello Dennis! Welcome to the forum!
The zoom buttons should always be visible, but they might be hidden when the list of charts is open above it for example. Please use pinch gestures to manipulate the zoom when this happens.
I can’t tell for sure without seeing a screenshot, but it sounds like the gray edges are most likely parts of the map that have not loaded yet. They should load quite fast, depending on your internet speed.
You can pin charts if, and only if, you have a flight loaded (1). This behavior directly corresponds to that of the web/desktop apps. When a flight is loaded and you look at the list of charts, you will see a “pin” icon beside each item in the list (2). Pressing it will pin it to the pinboard, showing below the list (3).
Hope this helps!