Can one serve in the US Senate or US House if convicted of a felony?

Answer 1

This is from NPR:

The answer, it seems, is a definite "maybe." U.S. Senate Associate Historian Donald Ritchie says that besides Stevens, only 10 other senators have been indicted while in office. Six were convicted; only one had the conviction overturned. None of the 10 was expelled by fellow senators. An expulsion requires the backing of at least a two-thirds majority in the Senate. Most either resigned to avoid expulsion or were acquitted of the charges against them before any action was taken by the Senate. According to Ritchie, the Senate can essentially do anything it wants with regard to indicted or convicted members. "The U.S. Constitution gives the Senate tremendous latitude to judge the qualifications of its members," says Ritchie, "and historically, the Senate's been very reluctant to expel such members." Instead, the Senate has generally preferred to wait for the appeals process to play out for a member convicted of a felony. A member such as (Ted) Stevens would most likely be "seated without prejudice" - that is, allowed to be sworn in once again, but subject to further action by the Senate if an appeal of his case is turned down. In such a case, the matter would most likely be dealt with by either the rules or ethics committees before being taken up by the full Senate.