Can we make our fluid domain object from a cylinder? I'm a beginner and wan't to know more about the fluid domain objects. Is it possible to make our fluid domain object from a cylinder? A lot of tutorials on YouTube use a cube for it. I have also tried to make my domain object from a cylinder but it's not affecting anything and I just want to make sure I did it right. Is cube really the base of a domain?
Yes, you can use Cylinder object as domain, but shape is not used in calculation, only dimension of the object (see Xylvier's answer). 

So just an extension ... if you need liquid inside cylindrical shape
- use Cylinder object as Effector (Physics Properties > Liquid).

Common problem is blocky colision (outer) shape.
You can solve it by using Boolean modifier > Intersect > Object - the same cylinder object.