By your interpretation, if a House member shot and killed another and a third member on the House floor in a speech said he saw the whole thing, he could not be questioned by the police or testify at the trial of the other house member. I do not believe this is the intent and I do not believe a court would interpret this section that narrowly.
Just my thoughts...
If another Congressman claimed immunity from testifying to a murder, he would be charged as an accessory to murder, or aiding and abetting.
To your first point, I'd argue that what Schiff knew is a product of his office, and so would be privileged. He only knew it because of what he was working on.
Of course, if he was working on treason then his privilege would be gone, but nobody is going to go there.
-PJ