Can infant formula cause eczema?

Possibly. A cow's milk protein allergy may present as eczema in infants. Other symptoms may include fussiness and irritability, bloody/mucousy stools, vomiting, and poor weight gain. Consider a trial of a hypoallergenic formula, but discuss this with your doctor first. Some will try soy-based formulas, however a number of children who are truly milk-protein allergic may be soy allergic too, so be cautious.
Yes. If a baby has an allergy to milk protein, yes one of the ways it can manifest is as eczema.