The first amendment has been interpreted to have exceptions that don’t protect violent speech, but what about this clause, could Congress members get away with saying literally anything during debates such as inciting violence or revealing classified information?
Statements made by a member of congress literally on the floor of their house while it is in session for legislative business are without doubt protected from prosecution elsewhere no matter how odious. Only congress itself (primarily the house in which they occur) could address these. This is in no way a provision intended to authorize unjustifiably extreme speech, but simply a safeguard to ensure that only congress itself, and not an external court, may decide what constitutes unacceptable speech in congress.
As such, all legal theory and case law around the "Speech or Debate" clause concerns not the content of the speech, but rather the context of speech that also qualifies as part of a congressional speech or debate, even though it does not literally occur on the floor in legislative session, is an action of research rather than statement, or might be practically executed by congressional aides rather than by the member themselves.
As a practical matter, when problematic speech occurs in congress, it is the presiding officer and members of the house where it occurs who are in a position to immediately do something about it, eg, rule the member out of order, halt their speech, remove them from the chamber, strike remarks from the record, or pursue disciplinary action such as censure or expulsion. And unlike a criminal trial requiring a unanimous jury, congressional discipline in the form of censure requires only a simple majority, and expulsion a supermajority.
Any ultimate criminal prosecution would have to rely on statements made in a context less obviously falling under this clause than actual floor debates do. Generally the clause is interpreted broadly in terms of furthering legislative purpose without consideration of actual content; but particularly odious external statements clearly intended to incite rather than further legislative process might cause reconsideration of the breadth To say something which would be elsewhere criminal on the floor, and on the floor alone, would seem a stunt of legal technicality unlikely in the face of its potential to be career-ending, even if not actually able to be criminally prosecuted unless repeated elsewhere.
It's also important to note that this clause applies uniquely to the legislative branch, and not to the executive.
Does the Speech and Debate clause protect members of Congress from prosecution for violent threats made during congressional debates?
While no case directly tested this, the answer is almost certainly yes, they are protected. As noted by SCOTUS in Gravel, which involved intelligence issues (see further below), as a general principle:
The Speech or Debate Clause was designed to assure a co-equal branch of the government wide freedom of speech, debate, and deliberation without intimidation or threats from the Executive Branch. It thus protects Members against prosecutions that directly impinge upon or threaten the legislative process. We have no doubt that Senator Gravel may not be made to answer either in terms of questions or in terms of defending himself from prosecution -- for the events that occurred at the subcommittee meeting. Our decision is made easier by the fact that the United States appears to have abandoned whatever position it took to the contrary in the lower court.
The CRS notes another relevant case, United States v. Johnson (1966) which involved a case of fraud conviction that relied on a speech given in Congress. The conviction was overturned:
It was not until the 1966 case United States v. Johnson that the Court embarked on an early attempt to define the protections afforded by the Clause in the context of a criminal prosecution of a Member. In Johnson, a former Member challenged his conviction for conspiracy to defraud the United States that arose from allegations he had agreed to give a speech defending certain banking interests in exchange for payment. In prosecuting the case, the government relied heavily on the former Member’s motive for giving the speech, introducing evidence that the speech had been made solely to serve private, rather than public, interests. Focusing on the admission of this protected evidence, the Court overturned the conviction. “However reprehensible such conduct may be,” the Court concluded that a criminal prosecution, the “essence” of which requires proof that “the Congressman’s conduct was improperly motivated,” was “precisely what the Speech or Debate Clause generally forecloses from executive and judicial inquiry.” The opinion noted that the Clause must be “read broadly to effectuate its purposes,” ultimately concluding that the Clause prohibits a prosecution that is “dependent” upon the introduction of evidence of “the legislative acts” of a Member or “his motives for performing them.”
Although overturning the conviction, the Court remanded the case to the district court for further proceedings, holding that the government should not be precluded from bringing a prosecution “purged of elements offensive to the Speech or Debate clause” through the elimination of all references to the making of the speech. The Johnson case therefore stands for at least two important propositions. First, the opinion demonstrated that the government is not prohibited from prosecuting conduct that merely relates to legislative duties, but is not itself a legislative act. When a legislative act is not an element of the offense, the government may proceed with its case by effectively “purg[ing]” the introduction of evidence offensive to the Clause. Second, though not explicitly articulating such a privilege, the opinion impliedly introduced the evidentiary component of the Clause by holding that even though a case may go forward, the Clause may be invoked by Members to bar admission of specific protected evidence.
However, in general, US Congresspersons do not enjoy immunity from criminal prosecutions, even while in office, and the extent to which the Speech and Debate clause applies outside actual proceedings of Congress (e.g. to aides or paperwork) has been litigated, fairly extensively.
Of some note here (same source) in Brewster (1972), the Supreme Court upheld a conviction for bribery, even tough the favor was a (protected) speech, namely a vote, which itself could not be entered into evidence. Merely accepting money in exchange for a promise for a was considered sufficient proof.
Turning to the terms of the bribery indictment, the Court framed the fundamental threshold question for any prosecution of a Member of Congress as: “whether it is necessary to inquire into how [the Member] spoke, how he debated, how he voted, or anything he did in the chamber or in committee in order to make out a violation of this statute.” With regard to bribery, the Court reasoned that because acceptance of the bribe is enough to prove a violation of the statute, there was no need for the government to present evidence that the Member had later voted in accordance with the illegal promise, “[f]or it is taking the bribe, not performance of the illicit compact, that is a criminal act.” Because “taking the bribe is, obviously, no part of the legislative function” and was therefore “not a legislative act,” the government would not be required to present any protected legislative evidence in order to “make out a prima facie case.”
In that sense, the Court distinguished the case before it from Johnson. Whereas the prosecution in Johnson relied heavily on showing the motive for Johnson’s floor speech, the prosecution in Brewster need not prove any legislative act, but only that money was accepted in return for a promise.
On the other hand, Congress may take actions on its own to punish its members, typically censure of explosion. There is an ancient case of expulsion from office (which is the equivalent of impeachment for legislators) for something perhaps related:
In 1797, Senator William Blount, Democratic-Republican of Tennessee, was expelled for treason, with charges centering on a plan to incite the Creek and Cherokee to aid the British in conquering the Spanish territory of West Florida.
You can read more on the Blount Conspiracy also on Wikipeida. Although expelled from the Senate, Blount was not criminally convicted, as far as I can tell, even though his questionable acts happened outside Congress.
Regarding the related q in body, regarding classified information, there are prior examples of that being deliberately entered in the Congressional record in order to effectively declassify it, most notably with (parts of) the Pentagon Papers. Stemming from that, there were lawsuits related to the extent that Congressional aides were protected under the Speech and Debate clause (Gravel v. United States ).
Only if not a case of rebellion or insurrection
Having been ratified later, the 14th Amendment supercedes Article I. Specifically, Section 3 of the 14th Amendment specifically prohibits a member of Congress from engaging in insurrection or rebellion against the U.S. Constitution:
No person shall be a Senator or Representative in Congress, or elector of President and Vice President, or hold any office, civil or military, under the United States, or under any State, who, having previously taken an oath, as a member of Congress, or as an officer of the United States, or as a member of any State legislature, or as an executive or judicial officer of any State, to support the Constitution of the United States, shall have engaged in insurrection or rebellion against the same, or given aid or comfort to the enemies thereof. But Congress may, by a vote of two-thirds of each House, remove such disability.
The matter is further codified in 18 U.S. Code § 2383:
Whoever incites, sets on foot, assists, or engages in any rebellion or insurrection against the authority of the United States or the laws thereof, or gives aid or comfort thereto, shall be fined under this title or imprisoned not more than ten years, or both; and shall be incapable of holding any office under the United States.