Might want to attach a blend file so it can be checked out
To be able to see your texture in texture mode, go to edit mode and then set the texture you are using in the UV editor. That should let you see the texture in texture mode after that.
I’m not sure about the issue you are having with the render. A couple thoughts are did you delete the original camera. If not, did you set the camera you are using to the active camera? (Ctrl+Numpad 0). Did you try to go to camera view while you had the sphere selected? I accidentally did that once with something else and wound up using the object i wanted to render as the camera (quite an odd situation).
I’m also not completely sure how far away that camera is from the object. It looks like it might be a little close, but that could just be me. You could check by hitting Numpad 0 and making sure the sphere is within the second rectangle.
On the field of view problem… you might want to elaborate on that. Your viewport locks on the camera? From the looks of it you aren’t using a default UI setup (either that or there’s a different layout in the new release that I haven’t checked out yet). You may want to pull down the user settings at the top and check the view & controls area.