Beitou? Is it east of Taipei? Beitun is near Taichung and I'm familiar with general geography there. Its pretty cool. I'd imagine if its near either of those two big cities they would do much better in the south, around Taitung
Yes, you have the right spelling.
Yes, Beitou is east of Taipei.
You can take the Taipei metro and then switch onto a train to Beitou.
Beitou is famous for its hot spring.
The park with the Engkala is really a very insignificant park with a small temple and the Engkala trees are planted on three sides of the temple.