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There isn't one specific role as a psychologist, since the details of the role would depend on the type of organization/company you are hired by. Many psychologists operate their own practice, so that's definitely one option. However, that will also entail some business background and/or some type of partnership with others that can provide specific skills to compensate what you offer. Many psychologists will also offer individual and/or family therapy to clients (which can be adults or youth), depending on the route/course you decide to pursue, within your path to a PsyD. Since psychologists often connect with a psychiatrist to practice their craft, it may not hurt to have some background in networking with others, developing business skills, and/or marketing, since those will come in handy as you run your own business.
If you are more interested in working for a company or agency, then it's likely you would get offers from hospitals, schools, clinics, and/or mental health organization or facility. I'm currently working for a large mental health agency, and we employ several psychologists, to offer counseling and psych testing to our clients.
To specifically answer your second question, yes, you will be able to work with teenagers as a psychologist, and many end up choosing that population.