Yes, smaller the mesh size, more accurate is the result. As Taif said, processing time will increase, because you will be including more mesh elements of smaller size. Also, mesh shape is important. Quadrilateral is usually preferred over triangular shape.

it depends on the type of analysis that you want to do, if it's a steady analysis for a beam you should'nt take a long time to find the compromized elemnts nembers to use