How can I color pasta during cooking or afterwards, preferably using natural coloring?
You are not stating whether you are making the pasta yourself or if you are using premade pasta. I am going to assume it is the former.

For red pasta, I would recommend substituting some of the liquids with beetroot juice. You will need to experiment with it to get the color right.

I would also recommend trying it in pasta both with and without egg, as the yolk will play a role in how the color develops.