You Do Need power plug adapter while traveling from Taiwan to Faroe Islands.

Here is Why You Need An Adapter

The outlet and plug type used in Faroe Islands are C, E, F and K and in Taiwan are A and B. This is how they look like.

Taiwan

In Taiwan, outlets of type A and B are in use.

Type A

Type B

Faroe Islands

In Faroe Islands, outlets of type C, E, F and K are in use.

Type C

Type E

Type F

Type K