In algebra when numerator is greater than denominator we often write down a mixed fraction eg. 11/4 = 2 3/4 Functions that operate with this kind of fractions are missing. Also the input method would be necessary. I suggest three text input fields appropriately aligned.
The second request is about the pane above the virtual keyboard. Often one expression is "in work" within several steps. An answer that comes out from program (let's say after you hit SOLVE) should be involved in next input. I know that clipboard is one solution, but it is clumsy. I suggest tap-and-drag. The answer is tapped and dragged to the next input line or somewhere else.
Also tapping on expression in input line could bring up a context menu: with "copy to new input line" and common (or expected) functions depending on the type of expression.
For implementing this request an intuitive approach could be used. Tapping on non-empty input or output line would select an expression and bring up context menu. If you don't choose from menu, you could simply drag selected item to new empty line or inserted it in an existent expression.
Mixed numbers are a bit difficult to work with in the sense that if you are not careful they can be ambiguous. For instance, 22 and 3/4 might be mistaken as 22*3/4. Plus outside of elementary school and cooking recipes I've never actually seen them used. Perhaps I am missing a vital perspective?
Thanks for the idea about the dragging input/output! I think this is a fantastic idea and will suggest it.
You can also use "ans" to refer to the last output.
For more advanced display see "Entry Bar Style" in "Interface Options". This will show numbered bars next to each entry. Then you can refer to specific entries using the "ans" function such as "ans(2)".