No, you would say passes both houses of Congress in that case.

Just don't like the immediate dismissal of the people's House when it comes to government affairs. When Congress does something it's important, regardless of the house it originates from.

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.