Basically, yes, on both questions. An AirTag is designed so that if you become separated from it, it will provide an alert. It is not designed to track people. Since, in both scenarios, the AirTag is not with you for a specific amount of time, anyone with an iPhone (with "Find My Network" enabled, will get an alert.) That alert would specifically tell them that an AirTag is present ... and is moving with them. So, for example, if one of your kids walks with their friends, they would get the alert. Alternately, if they don't have an iPhone, they would hear a sound.
The following support article should provide you with the details: