Should means there is a possible obligation (for whatever reason). Something is expected of you. Could means there is a potential capability. For sentence A, either can be correct: "what kind of gift should I bring..." is asking what is best to do in the situation, ie. what is expected of you, as Richard says. "What kind of gift could I bring..." is asking yourself what you are able to do, based on your resources (money, shopping options). I'd agree that "could" sounds more appropriate, and sounds more self-empowering. For sentence B, again go for "could" as it means you are able to bring pottery as one of your options. "Should" would mean you're expected by others to do that.

You "should" do something if it is required, expected, or necessary to be polite. You "could" do something if it is one of a number of possible things to do. In A, "should" works if you are wanting to know what gift is expected or polite according to custom. "Could" is better if you just want suggestions for a gift, and it appears more appropriate here. In B, "could" is better, because the person is suggesting a gift.