Paste your matrix as CSV with column headings in the first row and row names in the first column, pick a colour scale and value-label setting, then export SVG or PNG.
Use a grid: the first row holds your column headings, the first column holds your row names, and every other cell holds a number. That is exactly what you get when you copy a block out of a spreadsheet, so you can usually paste it straight in.
Sequential runs from a light tone at the minimum to a saturated tone at the maximum and suits data that only goes up, like traffic or sales. Diverging colours negatives and positives differently around a neutral midpoint, which is what you want for change, variance or correlation matrices.
Yes. Value labels can be turned on and the text colour flips automatically between dark and light depending on how saturated the cell is, so the numbers stay legible on both ends of the scale.