My older brother has some type of sore on the bottom of his foot and it has foot has swollen up. He is currently unable to walk on it. Could this be an infection?

Potential infection. Your instinct may be correct. Without being able to look at the sore, touching and feeling the skin around the sore and knowing more history - I would recommend a follow up with a physician. There is a higher risk for infections to the foot for people who have diabetes. Redness, swelling, warmth and tenderness around the area are all signs of infections. Again, I would recommend a follow-up.
Yes, it is Infection. You brother needs to seek healthcare from a doctor. If he does not have one, he should go the emergency room of the nearest hospital at the earliest.
Yes. This is suspicious of an infection and should be evaluated by a physician. Since the foot is so far away from the center of your body, its blood supply Isn't as good as the rest of the body and treatment should be begun promptly.
You bet. Could indeed have an infection, especially a cellulitis. He needs immediate medical attention. Do not delay.