These are questions that are going to take a long verbose answer to describe a simple problem.
First, you can easily change the “Done” button on the keyboard to “Next”. See: https://docs.coronalabs.com/api/type/TextField/setReturnKey.html
Pay attention to the Gotcha’s. On iOS, setting to “Next” will make it do what you want. On Android you have to manage the focus yourself using native.setKeyboardFocus() https://docs.coronalabs.com/api/library/native/setKeyboardFocus.html
Now if you want a row of buttons just above the keyboard, you would need to create that yourself using various display.* objects. There is no way to get the keyboard height but on iOS the hight of the keyboard is known values on various devices.
Now as far as showing the fields that get hidden by the keyboard, the best thing to do is to put all the fields into a display.newGroup() and if one of the fields that’s in the bottom half of the screen becomes active, in the event handler, move the group so that the next field shows.
Rob