The methane thing is a non issue. Where do you think the cows get the methane from? Plants they eat. As long as we keep enough plants to reabsorbe the methane for the cows to eat, and burp out etc etc then it's a closed loop. Like the water cycle. The issue is removing forests for cows.
Not really, the plant only binds CO2 from the air. The cow releases CH4 (methane), which is a much more potent greenhouse gas than CO2 is. Basically cows convert CO2 to CH4. I'm not sure about how much CO2 is captured vs how much CH4 is released over the whole process.
I mean everything exists in everything, the issue is what is their form. And cows convert methane in a very bad(for the environment) form. It's like burning down a tree, CO2 already existed in the tree but it was harmless. By burning it, you are releasing it in the atmosphere.