Yes. Yes. It is less common at this age due to less exposure, but still possible of course. This is especially true if the child has increased exposure, such as day care or older, school ages siblings.
Strep. Treatment with antibioticsimperative for people older than 18 months. We get receptors to acquire strep throat in the posterior pharynx between 18 months and 2 years old. Although infants may occasionally test positive for strep throat it does not have to be treated in these age groups. They cannot contract the sequelae of strep being rheumatic fever or acute post streptococcal glomerulonephritis.
Yes. It's a bacterial infection, so it can be contracted at any age. It's less common though.