We may not like the way North Korea is run, but it is not up to us to intervene unless their actions hurt the US, violate a treaty, or hurt one of the partners we have sworn to protect. We need to keep a close eye on North Korea's actions, but not otherwise intervene.
No, the US should not respond. The United States has friendly relations with South Korea, not North Korea. In fact, North Korea has been our enemy at times and they should deal with the crisis on their own. If the situation become intense and they need our help, then we should respond.
No, the US should not respond to North Korean officials being executed on the orders of Kim Jong Un. These actions have nothing to do with the US and only involve the North Korean government. If we choose not to mind our own business, we will only cause more problems between the US and North Korea.
The US being involved in any other countries' political or military actions shall not be permitted because our citizens are never told the real reasons that exists prompting our intervention. The US is ready to their strength and the solidity of their convictions but we must not accept the reason we are given for reaction is warranted without pubic investigations.