Will I get a refund for missed days due to flight delays?

If your incoming international flight is delayed by a day, you will usually not get any refund for that first night you missed, because the room was still held and the cancellation window has already passed. The hotel bills the agency anyway, no matter what.

This is exactly why comprehensive travel insurance is mandatory; you file the expense for that lost day to your insurance plan, not the nearby operator. The agency then makes a practical tweak and adjusts your airport pickup time so it lines up with your new arrival.