Is it rare for someone in their late teens to still have baby teeth?

Not at all. Often, the adult tooth that is supposed to replace the baby tooth never developed (very common in lower second premolars and upper lateral incisors), so an orthondontic consult is in order. If the teeth are prevented from erupting the unerupted/impacted tooth can cause a myriad of problems later in life. If the teeth are just "slow" then you should talk to your dentist about "helping them" come in.
Yes. You need to see a dentist who will take a radiograph (x-ray) to determine if you have a permanent (adult) tooth underneath. If not, then you may retain this deciduous (baby) tooth for several years or the rest of your life, with extremely good home care and professional maintenance.
Unusual.... ..But not rare. See dentist to determine if there is an impacted underlying permanent tooth. Perhaps orthodontic treatment would help get teeth to mesh better, because baby molars are larger that adult premolars, and can cause teeth to meet improperly, causing damage to the teeth and the underlying bone. Ask your dentist to check for bite problems as well as why that baby tooth is still there.