If my baby has a swollen scrotum, could he have a hydrocoele?

Yes. Most common cause of scrotal swelling in baby boys. Majority of them resolve sponaneously in first year of life. See a pediatric urologist or pediatric surgeon if the hydrocele gets large and tense, or it persists beyond age-1-year. Also if child has a fever or redness plus scrotal tenderness to rule out other pathology.
Yes. A hydrocele is a common possibility, but your son needs to be examined to rule out more serious causes including a hernia or twisting of the testicle, known as torsion.
Yes. Swelling that is tense and round is usually a hydrocele. Hernias are more ill-defined, and may be very large, and sometimes painful. Either one may occur on one or both sides. If the swelling comes on suddenly, it is more likely to be a hernia.
Possibly. The two considerations are hernia or hydrocele. See a pediatric surgeon to advise you. The hernia should be fixed, the hydrocele can be observed for a while.