Yes, this is literally the entire job description of a judge: to "judge" if someone broke the law. Details on what judges have jurisdiction over differ (in some countries they can't rule on constitutional matters), but this is basically how it works everywhere. You have appeals processes and whatnot to deal with mistakes. This is civics 101 separation of powers stuff.
What was issued was a temporary restriction from implementing the executive order until the matter is decided. No one issued an order declaring the executive order illegal.
You mean like the President? The President of the United States of America whom is deciding that parts of our constitution, our founding legal document isn't actually legally binding?
When that one person, who is part of the judicial branch and operating within its jurisdiction, has a trial placed in front of them? Yes. That's literally their job.
The quote is from a landmark case that established the judiciary as being the ultimate arbiters of the interpretation of the laws that have been passed by the legislature and signed by the executive.
