How can I patch a concrete porch that separated from the house?
From the two pictures, it looks like the porch is two parts - the foundation slab, and the top surface. Is the slab moving, or just the top surface? 

My suggestion would be to apply low-expanding spray foam (they make a grey-colored version so it doesn't look ridiculous, as well as one with pest deterring chemicals) to those cracks. If it expands too far out of the top-surface crack, trim it after it's try, then apply caulk to the face of it to waterproof it. 

Continue to monitor it for movement going forward. It's important to determine how and why you're getting movement.