Jongro BBQ

There are a few vegetarian entrees, but no grilling platter of vegetables. It might be worth a call to the restaurant to see if they could accommodate you, though!

Yes. There's an elevator

Yes, you can eat alone. You only pay for the food that you order, not for the table.

The staff cooks for you. Depending on how much you want, you can also just order more.

Both

I didn't see any halal options on the menu

The menu is largely grilled meats so there are foods that are naturally gluten-free, but I don't believe they have gluten-free sauces. The marinated meats are unlikely to be gluten-free. There is a variety of kimchi which is just different pickled vegetables (vinegar). They certainly don't have a menu section labeled gluten-free.

I take it you have never had Korean BBQ before... You should Google what Korean BBQ entails.

There is no bar area, so you'd have to occupy a table, if that's what you are asking. Thanks!