We took a taxi there.

No idea as we took a taxi from the hotel which is fairly cheap

take the high speeb train to zhuo yin and get down. walk into the mall area and you will see the ticket station and u turn left all the way to the end. take the travellator down. walk to the bus stop. do not cross the road. take the ha fu express at the first bus stop Nt 70 per adult per trip.

No admission fee for both places,

I'm sorry that I didn't see this earlier. Lotus Pond is a small recreational area with most of it's activities along the shore. There are no water tours of this pond. You can walk around the pond in about 2 hours if you don't stop but there are lots of religious areas around the pond that beds to be explored and photographed. So take your time and enjoy. At one point of Lotus Pond is a pavilion. On my last trip there I watched the local people in search of the Pokemon Go characters during the evening from my hotel room. It was a mad house and by late in the evening or early morning the gathering had disappeared. Have fun and enjoy.

It is free.

I would suggest that you get a taxi. The tower is not too far north of where you are staying so the fare would not be expensive. Looking at the map, it seems that you just get a taxi back, as the Liu Ho night market is not too far from where you are staying. Best wishes. James.