YouTube – How to Get a Custom Tab on Your Channel

The feed is, well your feed. It displays basically your activity. If you like a video it will appear in that feed saying you liked xyz video.

If you don't want the feed to be the default option that appears you can go into the settings when on your video channels page and check Enable featured tab*. This will make a featured video appear and videos uploaded appear below (of course only public ones).

No, unless the owner wants to do it there is no way that you could claim another username. just find another name, for example mybusinessofficial or anything else.

It may be helpful to read the YouTube's username trademark policy.

Problem is, they're probably not infringing your trademark, as you may know, just using a name doesn't infringe a trademark, what is important is "how" they use it. that said, if they even try to upload any content, similar to yours, which imply that their channel is connected with your brand, then you may use YouTube Trademark Complaint Form to take down their content, their account or assign it to yourself.