The short answer is yes. This can be confirmed by checking the front of the lens where the filter size is listed.

Take you lens and look the ring around the front element... you'll see what looks like a zero with a line through it, and the number to the right of that little symbol is the filter size, which will be the same size used for the lens cap that you'll need.

Yes, the Fuji 18-55mm has 58mm threads to accept a 58mm lens cap.

Yes, 82mm is correct.

Yes, the following lens cap will work with the sigma 70-200mm lens.

The Sensei 77mm Center Pinch Snap-On Lens Cap has smooth and flat slots for gripping the lens cap, but I would not describe them as slippery. It is easy to grip and take off of the lens, but is secure when attached to the lens.

The Tamron 16-300mm f/3.5-6.3 Di II VC PZD MACRO Lens uses 67mm filter threads, while the Tamron SP 150-600mm f/5-6.3 Di VC USD Lens uses 95mm filter threads. As such, the Sensei 67mm Center Pinch Snap-On Lens Cap, B&H # SELC67, would work on the Tamron 16-300mm lens, but the Sensei 95mm Clip-On Lens Cap B&H # SELCC95, would be needed if you need a lens cap for the Tamron 150-600mm lens.

Yes, the Sensei 40.5mm Center Pinch Snap-On Lens Cap will fit on top of any 40.5 mm filters.