On the last question: a guess

The folks who breached the doors and barricades quickly rushed down hallways to get Pence or whatever. Many of the security folks rushed to protect or whisk away the Senators and Representatives.

With the doors open and much of the security forces away from the entrances other members of the "crowd" strolled in and many did, indeed, act like tourists.

The remaining security folks couldn't push them all out, so they let them mill about as long as they didn't seem to be violent. It was a calculated risk, based on a situation which none had anticipated.