I would like to know if public strings, that are getting updated every time a user taps on object, (Once every two seconds MAX) will effect the performance of the game on iOS? Should i make these strings private? Or does it not matter?
It matters in the sense that each string that is changed creates garbage (the old string), which Unity must then, at some point clean up. This is called Garbage Collection, and every time it is done it takes a lot of CPU time, so the user might notice lag.
You should consider using the System.StringBuilder class for strings that are frequently changed, because it does not create garbage.