How to control a cellphone using an Arduino?
If we make a number of assumptions we can describe how to go about using a Arduino Nano to control a cell phone keypad with no or minimal additional hardware.  If you find the assumptions are not valid you will have to do some work to find a solution.  A standard way to design a keyboard is to place switches on a wire grid such that they short a "row" wire with a "column" wire.  The most efficient way to arrange switches is in a (near as possible) square grid.  So we assume a 5 by 5 grid is used for 25 switches.  Further we assume the rows are "scanned" and the column are "sensed" and that the logic voltage is compatible with the Arduino Nano.  Finally we assume that the phone will scan the switches much slower than the Arduino runs such that we can sens a row voltage change and, in turn, drive the column voltage fast enough to emulate a button press. If all these assumptions are true, then we need to configure 5 Arduino Nano pins as inputs.  One for each row.  And 5 Arduino Nano pins as output.  One for each column.  To activate a fake switch we wait until the row which contains the fake switch is activated.  Then we drive the column active which contains the fake switch.  There are many more details which you will have to work through. For instance, the phone will likely try and debounce the switch closure.  So a fake switch will likely have to remain closed for many cycles of the keyboard scan.