You can only claim a hamlet if you already have a mayor title, something that is no longer available for purchase. Your only bet at this point would be to have a bloodline or higher pledge package and to get a title during the Settlers of Elyria event.
You would have power as basically the chief executive of that settlement
Yes, people can spark into existing characters in your settlement unless they are all claimed by people you know already, if someone wants to come settle in your hamlet they would need somewhere to stay which you would have some influence over as the "executive" of that settlement.
Having a certain number of people in your hamlet is a requirement to Create said hamlet. If you claim one then it is assumed it already meets these requirements, and until sparked into the population will be made of npcs. For more info on establishing settlements you can click here and read the portion that outlines "Aristocracy & Establishing Settlements"