The smoke lens are polarized on the black frame?

There are both polarized & non-polarized Dark KD's. Right now, the 20% larger KD's, the X-KD's polarized Smoke lens are ASIN B00EQDIMSO. The polarized dark grey, original size ASIN is B00I4DYES4 & B001V3959W. The X-KD's smoke lens ASIN is B00BGH1XH0. The larger, but similar style, Blues Brothers ASIN is B002JFEETW. Nobody is bait/switching anything. The problems start when sellers who don't know what they're doing come in and create duplicate listings, and screw things up. Then sometimes Amazon screws things up further when they try to get them straightened back out. It's a constant battle. Also, some sellers include the microfiber pouch, some don't. The only one I can vouch for that includes the pouch is Value Vortex. Hope that helps.

Are they shipped in a box?

They are safely packed and shipped. They came in perfect condition. If you mean, an individual case, no case included.

If I ask for it to be send to an hotel, can the receptionist receive it and send it to my room?

That is something that Amazon would have to answer if you are buying from an FBA seller; as Amazon stocks and ships the products. I called them and asked. They said "yes; as long as the buyer is going to be registered at the hotel at the time of delivery, it can be done." That's what they told me, anyway! :-)