Ok…the first thing you need to understand, is there are several investigations going on, simultaneously. The House Intelligence Committee, which Rep. Schiff is the ranking member of (which means, he is the leader of the minority in that Committee), is one of the. There is also one going on in the Senate counterpart, as well as one in the Senate Judiciary Committee (which oversees things like…the DoJ, and thus, the FBI). These are all Congressional investigations, and don’t actually have an prosecutorial power…if they find wrong doing, they have to submit their findings and recommendations over to the DoJ to prosecute.
Since these are Congressional, they are by nature, political. And the majority party can “shut down” any or all of them, because they have the votes (in theory). There would however been TREMENDOUS backlash to such a move (doing such political moves comes with a political cost), and given the backdrop of it being increasingly likely that the republicans lose the House…that could lead to some very bad consequences for republicans.
Then we have the Special Counsel investigation, led by Robert Mueller. Mueller was appointed after the head of the FBI, James Comey, was fired by Trump. The FBI under Comey was conducting several investigations into numerous people in the White House at the time of the firing…some of these were counter intelligence investigations, some of these were criminal investigations. The Special Counsel has essentially taking over all of the criminal investigations that were being done by the FBI, as well as expanded into more criminal investigations. The Special Counsel, however, largely uses FBI agents to do a lot of their investigative work.
The President cannot fire Mueller directly. Normally, the Attorney General would have that responsibility, but AG Sessions has recused himself (because he is under investigation), and his deputy, Rosenstein, now has that responsibility. But its not an “at large” power, meaning, Mueller can only be fired “for cause”, and the rules regarding the Special Counsel are very specific as to what causes would be allowed.
The Special Counsel investigation is NOT something either party in Congress can shut down. It is non partisan and unbiased run by professionals. The non partisan and unbiased part are the parts that some republicans are now attacking, under guidance from the White House. Since Trump cannot directly fire Mueller, or realistically remove him without causing an even bigger firestorm, they see their path forward is to question the credibility of the Special Counsel. That is what you are seeing playing out now.
Coincidentally, the rumors around D.C. is that another big indictment is about to land. This makes this sudden escalation in these moves all the more suspicious.
Hope all of this helps. Good luck on your assignment.