No, they are separate: The Bundestag (the more prominent and more widely known institution) is a parliament on elected the federal level. The Bundesrat is made up of representatives sent by the individual state governments. The Bundesrat acts a a check to the Bundestag, as it has to approve laws proposed by the Bundestag before they can take effect.
I might hav missed some details but that's what I can remember right now.
Really? Which Protests do you mean? The vast majority of German flags I saw on anti Nazi demos in Germany had been mounted to Buildings or the hands of some Nazi Idiot at the counterprotest.
Going one step towards the center of the political spectrum from the firmly left learning anti Nazi Demos, there are the anti AFD Demos which also attract(ed) people with far more moderate centrist political views than the average Antifa member, thus being more likely to support the idea of the state of Germany in its current form. Still, most flags you'd see were for pride / lgbtq+ or political organisations.
You might see a German flag from time to time but i think it's just plain wrong to call it common.