The constitution contains rules for how the government should operate in normal times. It can't provide for every eventuality, or for every emergency situation. While the constitution does give guidance for how government should proceed in some situations (for example the 25th amendment provisions for the removal of a President who is unable to discharge the powers of the office) There is nothing for dealing with the situation in which only one congressman remains alive. What would actually happen is the constitution would be suspended, the President and military would have de-facto powers to govern until whatever it was that killed off all the other congressmen was dealt with, and then there would be some kind of emergency elections leading to a re-establishment of constitutional government.
Some facts are clear, even in the current constitutional arrangement. No the lone survivor could not claim to be "Congress" Any legislation must pass both houses and the survivor could not be both a representative and a senator.