In what way, if any, does Congress control or regulate the judicial branch of government?
The answer depends upon which part of the federal judiciary you are asking about, the Supreme Court or the district and circuit courts below, and I should also point out that legal scholars disagree with one another on this issue. All we really have is the Constitution itself to guide us, with little from our Supreme Court on any congressional control of federal courts that is precisely on point.
It is Article III, Section 1 of the United States Constitution that creates the Supreme Court and provides for the creation of the courts below it:
The judicial power of the United States, shall be vested in one Supreme Court, and in such inferior courts as the Congress may from time to time ordain and establish.
This has been held to mean that the Supreme Court is created by this article, while it is Congress that may create "inferior" courts. This implies that Congress can do little to control or regulate the Supreme Court, with two notable exceptions.
Congress can refuse to appoint a president's proposed candidate for the Supreme, and as we are seeing now, they believe they are entitled to not even consider a proposed candidate. They can also impeach a Supreme Court Justice.
Most legal experts argue that Congress cannot limit the jurisdiction of the Supreme Court, which is laid out in Section 2 of Article III, but there is substantial disagreement upon whether or not Congress can limit the jurisdiction of the lower courts, which is called jurisdiction stripping. And some experts argue that because Congress creates the lower courts, it could dismantle them, too, or reduce their numbers, or consolidate into fewer judicial districts, a kind of "We brought you into the world so we can take you out" argument. And Congress has threatened to do this from time to time.
Most questions regarding legal matters have the answer of "this depends," and I hope this does not discourage you from continuing to be interested and curious. This question is unusually susceptible to this answer because we have so few rulings on this issue. Law reviews are filled with articles supporting the contention that Congress can do what it wants and filled with articles supporting the contention that Congress can do very little to control the inferior courts. Perhaps you will go to law school one day and write your own article on this issue!