Yes, but its customary to buy a cigar or two, or food and drink. If all you're doing is smoking a cigar you brought in, they'll charge you a cut fee.
Generally you are allowed to, but it's seen as rather rude to the shop. They may charge you a couple bucks as a 'cut and light' fee
You can bring your own cigars.
You should call to ask them that question. It looks like you need to buy them there, and I think you can store them there.
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