Is there a way to check mental retardation symptoms?

Yes. There are developmental milestones joe children. If a child is behind, there i'd cause for concern. There is specialized neuropsych testing.
Yes. If you are worried about a child who is not making progress in school, a psychologist should then test your child's iq, memory, handwriting, and achievement scores. A physician can then assess for a cause, if present.
Pro evaluation. Gosh, a good evlauation probably by a child neurologist and at least a chidl psychologist or neuropsychologist would be needed. Deficits in one or more areas could reflect limited globa intelligence or be part of a far, far more complex neurodvelopmental or neurological condition. Usually an iq test as well as a formal adaptive behavior measure is needed for classification purposes.