Is it possible my 16-month-old is speaking in advanced sentences, or am I hearing things?

If his speech sounds like he is putting words together, then he probably is even though it sounds a little garbled. You are probably with your child more than anyone else, therefore you will be able to understand his speech and what he means even though it may sound garbled and like he is speaking martian to others. LOL! My 18 month old will sometimes say "this is" or "it's a" before a noun. For example, she will point to a book and say "it's a book". It sounds like she is saying "isha book" but my husband and I understand exactly what she is saying. When she says "this is" it sounds like "dis is". I think your son is definitely more advanced than other children his age in his language skills. Read to him a lot, walk around the house with him and identify everyday objects and try to get him to point at the object and repeat you, and when he says new words reinforce his accomplishment by repeating the word he says back to him and praising him. This will encourage him to continue his language development.