Yes, they can. But since you can't register for an EC account if you're under 18, they can only do this as part of your HH account. There are several people on here who have children with Silver/Gold status...and one person (but I forget who) who has a child with a higher tier level than them
Same earning rules and rates apply based on fare class (surely if the elder one has been travelling for a while and earning points, you can check if they're posting OK to his account yourself, and at the same rate?). They can't enter lounges alone on their status, but the extra card can be useful if you're all going in together and want to bring extra guests.
Phil