No, I don't. But it could be that I'm not fluent enough in these aspects of Photoshop. I've had good luck leaving the three boxes checked.

10mm Nikon is not a fisheye, even though 16mm is. It's the lens design that determines the perspective.

No. I leave it checked and use "bicubic smoother" to enlarge the image.

I would do both. First, resize the picture to 360, then in the print dialogue, select to fit the media you are using.

I don't think you're wasting you money on the Tamron lens. I borrowed one for a week and got better contrast, excellent edge-to-edge sharpness than with my Nikkor 18-300mm, and quick autofocus at 600 (900 dx) mm. I was very impressed, and at the risk of getting some GAS, I ordered one to go with my D7100.

KEH camera will repair any lens for $195. That includes shipping back to you. Worth a thought.

A particular note for those photographing in Washington, D.C.: You need permission from the Architect of the Capitol in order to shoot pictures of the Capitol building ON A TRIPOD! I found this out one day some years ago when attempting to do just that with my wide format, shift-lens camera. I managed to get a couple of shots before being confronted by capitol police.