Yes. Generally tomato paste is added to (1) give a tomato flavor, and (2) to thicken the sauce/soup/etc. You can definitely add tomato sauce, ketchup, fresh tomotoes to give a tomoto flavor (though all three will give slightly different flavors than one another). Since ketchup, tomato sauce, and fresh tomatoes all have more liquid than tomato paste, they won't thinken the liquid as well. So just reduce the liquid in the recipe a little bit to compensate.
For example, if you mix a teaspoon of tomato paste with a cup of water, you get something that has about the same consistency as canned tomato sauce. So you could use canned tomato sauce in your recipe in place of one cup of liquid and a teaspoon of paste.
Katchup is thicker than sauce, so you wouldn't have reduce the amount of liquid as much if you use it. Plus, katchup has vinegar in it, so you might want to reduce the amount of vinegar you add otherwise. For point of reference, I've seen Jacques Pepin add katchup to sauces many times.