We didn't take brkfast since right outside hotel you get best street food.

Hello there! Shilin Night Market: From the hotel, head to the nearest metro station (Ximen station). Take 1 stop to Taipei Main Station, and change to the red line, towards Tamsui/Xinbeitou. Alight at Jiantan station and it's a 5 minute walk away. Taipei 101: From Ximen station, take to Taipei Main Station again. You're changing to the red line again but head towards Xiangshan. Alight at the Taipei 101 Station/World Trade Center station (it's the stop before the terminating stop). East Dragon Hotel is a family run hotel, so I don't think they help to purchase attraction tickets for guests, but I'm sure they can give you suggestions on where to go. Also, I believe there's no need to book any day tours to explore Taipei as it's fairly easy to figure out how to get to places. The metro staff are very friendly and speak fairly well in English and the receptionists at the hotel are knowledgeable too, if you need any help. Lastly, there is a bus service provided by KuoKuang Motor Transport that takes you from Taoyuan Airport to Taipei Main Station for TWD125 (might/might not have changed) per adult, so maybe you can seek that out. However, it'll be easier if you just get the reception to book a taxi to pick you up at a specified time as I assume you'll have some luggage when returning to the airport. A ride to the airport will take approximately 1 hour. Not very sure about the price now, but I'll guess it's upwards from TWD1000. Hope this helps!

Ximending Area where East Dragon Hotel is located is in the city center of Taipei. For airport to hotel transfer you can book through KLOOK, it is cheaper than taxi and more convenient because the driver will wait for you at the exit with your name. As for early check-in you can discuss it with the hotel receptionist since they can speak english well. As for the two discontinuous days, I think you need to book it separately, then you need to check-out in the morning of April 17 and leave your luggage in the concierge. You can get it back when you comeback on the 18th to check-in again.