***** NOT A TEACHER *****
In my opinion, I believe that you can, indeed, say "Here's the ..." and "What's the last ...." without "any problem" in ordinary American conversation.
This is especially common with the word "there."
"There's a lot of people in the cafeteria today."
"There's four books on the table."
"Hey. look! There's Mona and James!"
In conversation, we tend to speak fast. So I feel that many native speakers do not want to take the time to pronounce "are."
Another reason may be the fact that it is difficult to pronounce "there're" (the contraction for "there are").
OF COURSE, in formal writing (a business letter or a report for your teacher), it would a good idea NOT to use 's for are.
Student or Learner