What could be a reason that a 19 year old female is experiencing memory loss and forgetfulness? Can anxiety play a role in that?

Memory loss. Anxiety is one of many possible causes of memory loss in a teenager. Other possible causes are alcohol, drug use, medications, stress, head trauma, sleep deprivation, epilepsy, infection, hormonal abnormalities, etc. See your pcp for exam to rule out medical causes for your memory loss and forgetfulness. I hope this helps. Best wishes.
Yes/many things. A person performs at their best when they are well rested, healthy, properly nourished, and in a comfortable setting. The opposite will diminish performance.Anxiety plays to the comfort issue and it's effect can be major, but all the listed factors must be addressed to sort this out.Write down a good history & questions (so you don't forget) and go see your doc.
Yes could be. But consider not only emotional stress, anxiety, depression, but also poor sleep, use of recreational drugs or alcohol, medication reactions, nutritional issues, thyroid problems, vitamin deficiencies.