1. Which everyday objects are like cylinders?

There are many objects in a cylindrical shape. e.g. Cans, water tanks, mugs, gun barrels, spa pools, bottles.

2. Do the ends of a cylinder always have to be included when finding the surface area of a cylinder?

It depends on the wording of the problem.

If you are finding the surface area of an open-ended pipe you would only need the curved part of the formula
2πr h.

If you are finding the volume of a solid object in the shape of a cylinder you need to use 2πr2 + 2πr h.