Artice I, Section 6
Regarding the privileges of Congress:
They shall in all cases, except treason, felony and breach of the peace, be privileged from arrest during their attendance at the session of their respective Houses, and in going to and returning from the same; and for any speech or debate in either House, they shall not be questioned in any other place.
This covers McKinney (assault is a misdemeanor.) So yes, she could have walked up to the officer, smacked him across the face for no reason whatsoever, and gone about her business. And not been arrested for it, per the Constitution. The law is different for Members of Congress.
If you're unhappy about that, and I can see where some would be, there's a procedure for changing it. It's tough to do. In fact, it's only been done 17 times in 218 years.
As to Senator Webb, I'm not sure if possession of an unregistered firearm in DC is a misdemeanor or a felony. Can a municipality even define a felony? But it's also been posted here that members of Congress are allowed, by statute or custom/rules, to possess firearms within the confines of the Capitol (which is not within the jurisdiction of the DCPD, which is why the Capitol PD exists.) In fact, IIRC, the Capitol and White House are not technically in the City of Washington, DC. So DC law wouldn't apply in that case.
The staffer could have committed a DC crime when he (I'm assuming) transported the Senator's firearm across the city to the Capitol, but the arresting Capitol PD officer wouldn't be authorized to arrest him for a misdemeanor he did not witness, at least as I understand arresting powers.
Again, I'm assuming here, but I think that the staffer was arrested as a security precaution, until they could figure out that he was who he said he was. There's a lot of staff people on the Hill, and the CPD can't memorize them all. There not going to take someone at their word.
"Oh, that's Senator so-and-so's gun, I work for him, and I'm just bringing him this bag."
"OK, sir, please place your hands behind you back."
--Shannon