One of the first to use letters as parameters in equations was Francois Viete (1540 - 1603). So use of letters in mathematics as variables, general numbers, and later for other things such as functions, operators, vectors, etc. started in renaissance. 

One of the advantage of such use of letters is that we can write short, clear and unambiguous formulas e.g. Vieta's formulas for sum and product of solutions of quadratic equation. Before the use of letters in mathematics, mathematicians didn't write formulas, they would explain the formula with words. Pythagoras never wrote `c^2=a^2+b^2` but he said: "In any right-angled triangle, the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares whose sides are the two legs." 

The letters are variables.  If you use a number, you would just get confused.  The letters x and y were chosen because they do not really look like any numbers.  We began using n when we started teaching algebra to younger kids, because it made sense to them that n would be number.

I don't know this for sure, but it just makes sense.  In algebra, you of course have variables for which you don't know a numerical value.  So you can't use a numeral to represent them.  If you're going to have them in an equation, you have to represent them with something.  Letters seem more of the obvious thing to use than random symbols that you'd have to think up and draw over and over.