Meaning of peer review
When people say "peer review" in regards to a scholarly work, they are implying they refer to the "scholarly peer review process", not to some generic review by peers in the general sense of the meaning of the individual words "peer" and "review".
This process refers to review by your scholarly peers, not related to any age group, conducted though journals/publishers who assign reviewers to assess the paper and make editorial decisions about whether to publish the paper or not based on their recommendations.
Looking over your manuscript before submission is not "peer review" in the academic sense. You don't want to say that your paper went through "peer review" just because you had some peers (or even people who are you senior) look it over.
Acknowledging help on a paper
It may be appropriate to thank people who have helped improve the manuscript but haven't contributed enough to qualify for authorship; this section in papers is called the "acknowledgements" section. It can include statements like:
The authors thank J.A. Professor for helpful comments on a draft of the manuscript.
Sometimes authors will also thank people from the peer review process anonymously if suggestions raised in peer review are particularly important for the final paper, but it's not necessary or typical to thank reviewers in general.
It's polite to ask permission to acknowledge someone by name before actually mentioning someone in the paper (they may feel uncomfortable with it and ask to not be named if they either don't support the work or feel they didn't do enough to warrant it), and it's certainly not good to try to add acknowledgements because you think it will somehow help your paper get accepted (nor because you think it will make your non-published preprint appear to have been somehow validated and judged as correct by experts), only when people genuinely deserve the credit.