Does the hotel offer shuttle service to/from airport?

No but you can take the tram and be to the airport in 20 min

I did not see a shuttle but it is only about 15 minutes away from the airport so you can easily get an Uber or lyft for a reasonable price.

I recommend you call the hotel. They can orient you on transportation options. In my case, I had a small size wheeled suitcase, so I walked to the train stop and from there took the line to the airport. Good luck!