It's normal to release the brakes to take the brake plate out of the hub.
You don't have to take the chain off the bike but do need to take the chain off the rear sprocket. After you undo the axle nut and the brake link, slide the axle forwards to slacken off the chain tension and it will usually come off the sprocket.
I see at least one missing rear wheel spoke.
Yes it's common to fit a tube in a tubeless tyre. That rim/tyre combination won't hold air pressure without a tube.
You will need to set the wheel alignment and chain tension when you put it back together. You can make a mark if you want, but are you sure it is set right at the moment?
That dodgy-looking brake return arrangement is to stop the brake sticking on so you may find that there are problems inside the brake hub that are causing it to stick on (missing/wrong spring, worn linings, worn brake drum). Looks like someone has extended the length of that brake arm too.