McLinko is a web app that allows you to find broken links on the YouTube platform.
This happens occasionally, usually with Facebook and LinkedIn. Because those websites require you to be logged in, the page Mclinko is checking may not be visible to the outside world. ie: It has some privacy set up.
No, Because you have created a YouTube key and API, you are using the legitimate way to search YouTube. There is a limit set by YouTube for the number of searches you can do.
You can find that information in their Developer Documentation