Hi Allen,
I see some confusing code formatting that may be contributing to your problems.
For example, not sure what your trying to do on this line ..
if (byte(BTSerial.read() == 'A'));{
but I think its just plain wrong. Unless your aware your going for some advanced coding, you have the conditional check of "BTSerial.read() == 'A'" inside the cast of byte(). This would mean you want to case the true/false value to the byte cast function; but then your not even using the byte() cast in the if() ... its just thrown away. If you just trying to compare the read() to character 'A', then you just need ..
if(BTserial.read() == 'a') {
Then further on that line you have a semicolon ; between the end of the if() and the open curly bracket {. That is an odd place for a semicolon and I assume its misplaced.
There's nothing wrong with the String declaration, it complies just fine "String readString;". Any errors your getting must be related to some misplaced bracketing above that.
I would start by comment out most of that code until you get to a clean compile. Then start adding back in a few lines at a time and keep verify/checking to see what starts giving you problems.