Coats and hats would be "merch".
Shakes, malts, burgers, fries, would be "food".
Some places may even offer "services".
Bar is always separate.
To answer your last question YES legally you can carry at your local bar, provided just like any other private property the ownership/management does not say no.
***Liquor license, CPL, alcohol sold for consumption and primary source of income, OC only.
Probably better OC if it is a Bar. Many people here go to bars for food and company not just booze, and many myself included carry in them.
If you do and you run into management that wants you to leave, be polite and do so. I would not feel obligated to pay my bill, but I would tip my waitress/waiter. If you feel comfortable and want to continue going to the venue we can help you to educate management / owners and some change their minds.