Not necessarily. In the US traditionally the House Reps are referred to as congressmen (unlike the rest of the world) and the Senate, senators. So sometimes Congress is shorthand for the House. Though I agree it shouldn’t be.
This is false. Traditionally, when only one chamber of Congress passes a bill, headlines explicitly state which chamber. "The House passed a bill that..." or "The Senate passes a bill that..."
The OP is correct that Congress implies both chambers. Yes, "Congressman" or "Congresswoman" refers to House members. But the headline says "Congress".