If you want the x -axis thicker, double click on the y-axis and then add a reference line whose value corresponds with the value of the x-axis line that you want to be thicker. You then increase the thickness by increasing the value of "Line Style" in the Y Axis Setting pop-up. You can also change the color. This will overlay your selection over the existing x-axis line.
I don't think you can do anything with the chart border other than have it selected or not selected in your preferences.