Does the hotel provide shuttle to and from the airport?
No direct pick up by the hotel, but it can be arranged. Suggest that you look confident and take a yellow cab from outside the airport.
They do not. I booked with Expedia and used an independent company called Baron Travel. However, the hotel does have private vehicles and if you call them in advance, they will pick you up for a fee. This fee is higher than Baron Travel's fee. So, call the hotel in advance to make arrangements.
No. Most hotels in the Metro Manila area do not provide a shuttle service. Many would provide a take-like service with higher charges normally than a regular taxi. Hence, it might be better (and just as safe) to pick up a taxi from the airport. If you want to feel more safe/comfortable, just call (or act like you are calling) a friend and say you are in a taxi number ---- expecting to be at your destination in --- minutes.
Get an answer from The Linden Suites staff and past guests.