aspick:
I have been told by my proffessor that my syntax is wrong in many places
He's obviously right - that doesn't even compile, does it?
The use of if/else if in the output functions is redundant, and it would only take a tiny effort to convert those dozens of lines of output code to a few constant declarations defining the segments on for each digit value and defining which pins correspond to which segments for each display digit, and some common code to output the set of segments states to a specified digit.
You could do with testing this code, too:
y=number%10;
x=(number/10)-y;
Once you get it working, note that it will produce numbers in the range 0 - 9 not 1 - 10 so your switch cases need correcting, and you need a break after each case.
The variables pin0 .. pin13 are (a) pointless, because the names tell us nothing more than the original number itself did, and (b) should be constants not variables.
I can see this is just an early project for you and although it's got quite a lot of issues at the moment I'm sure you'll soon get the hang of things, but I suggest that instead of writing the whole thing in one go and then wonder why it isn't working, you would be better off building up your sketch in small increments and test each part as you go. Is your analog read returning the values you expect? Can you convert the return value into two digits correctly? Can you output the digits 0 - 9 in the first position, and in the seconds position? Finally, can you add all those functions together into a working sketch?
During testing you'll find Serial.println statements hugely useful to let you see what's going on inside the Arduino, so you should consider leaving the serial pins (presumably 0 & 1) free so that the serial port works and connect those segments to other pins instead.