A1Notation conversion to row & column index
I see you fixed the index-checking/defaulting bug that gengkev pointed out in the comments. As SpiderPig mentioned the cleanest solution is probably index = index ? 1 : 0.

However, I don't know if I'd bother with the index parameter at all. So far, it's led to bugs, duplication across all three functions, and all it really does is add/subtract 1. That can be done anywhere.

So I'd recommend just translating to 1-based indices, and if you need zero-based indices, well, subtract 1. 

I wouldn't worry about using a regex - but I'd probably make it stricter. I imagine that a cell reference isn't that flexible. I imagine the string may contain "$"s but that's about it. Correct me if I'm wrong.

However, cellA1ToIndex() also does too much. It checks things that the other two functions don't. So if you call the other two functions directly, your input isn't checked as strictly. For instance, colA1ToIndex() will accept a string like "%#", and return something wrong. Similarly, rowA1ToIndex() will gladly accept just about anything, and return NaN.

So I'd keep cellA1ToIndex as "dumb" as possible, and make sure the specialized functions are more robust.

Lastly, why a of maximum 2 letters for columns? Why not 3? Or 4?

I'd do something like this:

function cellA1ToIndex(cellA1) {
  var match = cellA1.match(/^\$?([A-Z]+)\$?(\d+)$/);

  if(!match) {
    throw new Error( "Invalid cell reference" );
  }

  return {
    row: rowA1ToIndex(match[2]),
    col: colA1ToIndex(match[1])
  };
}

function colA1ToIndex(colA1) {
  var i, l, chr,
      sum = 0,
      A = "A".charCodeAt(0),
      radix = "Z".charCodeAt(0) - A + 1;

  if(typeof colA1 !== 'string' || !/^[A-Z]+$/.test(colA1)) {
    throw new Error("Expected column label");
  }

  for(i = 0, l = colA1.length ; i &lt; l ; i++) {
    chr = colA1.charCodeAt(i);
    sum = sum * radix + chr - A + 1
  }

  return sum;
}

function rowA1ToIndex(rowA1) {
  var index = parseInt(rowA1, 10)
  if(isNaN(index)) {
    throw new Error("Expected row number");
  }
  return index;
}