This King of Judah was protected by the High Priest. He was anointed and proclaimed King on a Sabbath day. Who was he?

He was King Joash of Judah

Source: 2 Kings 11-12 2 Chronicles 22-24

It was only mentioned in Acts 1:12 How long is a Sabbath day’s journey?

It was 2000 Cubits. That translate to 1000 yards or 914.4 meters. It was the distance that separated the Ark from the people when they marched.

Source: Joshua 3:4

The Sabbath was taken seriously. What was the penalty for working on the Sabbath?

The penalty for working on the Sabbath was death. This actually happened in Numbers 15:32-36.

Source: Exodus 31:14,15 Exodus 35:2