InsertCell Doesn't Work As Expected In Firefox/Chrome

I have a table that looks like:

And a function to add a row and cells in the row that looks like:

The problem is the insertCell won't insert that first cell with an x in it (which will allow users to click on the x button to delete the row) in the first cell in Google Chrome. Firefox inserts a row with the first cell containing the x button but no other cells with the text boxes.

I've tried setting the index on the cell insert to 0, 1, 8, nothing and Chrome either inserts a row with nothing in it (no text boxes, no x button, nothing other than a slight addition of space below the title row) or it adds the row correctly except the x button always winds up in the last cell. IE adds it correctly with no index value or 0. Firefox needs the 0 index (no index creates a blank row with nothing in it. It looks like there's a tiny blank row of nothing being inserted because you see the table get a tiny bit larger vertically but there is no x button, text boxes.

What am I doing wrong? How do I make this work in all 3 browsers? Well actually all browsers ideally but....

Further, if I supply the 0 index to get a row, clicking on the x button to delete it works correctly in IE and Chrome but does nothing in Firefox.

That code looks like:

So what is wrong with both the addRow and removeRow functions that is causing Chrome and Firefox to behave incorrectly?