The legal status of the affiliate depends on the terms of the agreement underlying the respective affiliate program. Up to date, it is not clear what kind of contract the agreement is. In my opinion the affiliate can not be regarded as a merchant since affiliate programs seems to be like some sort of sponsoring. Consequently, under German laws, an affiliate needs no trading licence. Anyway, the revenues generated from affiliate programs are in general not sufficient to earn someone's living.
Most national laws provide for some level of less protection of minors.
For example, under the German Law a minor can conclude a binding contract as long as the deal is advantageous for him in both ways, legally and economically. Should you require legal advice, please consult an attorney. While we cannot vouch for the accuracy of the web, we have located some web-sites that may be of interest to you. The precise nature of the affiliate in an affiliate program is as variable as the affiliate programs that exist on the web. Presumably these affiliate programs would have age requirements.