How does peer review assess the validity of experiments carried out?
Does the peer review process ensure experimental data being reported is accurate and how so?

At very least, the peer review process is not designed to catch intentional fabrication because reviewers are only asked to read the manuscripts.
That being said, intentional fabrications sometimes get caught during the review process if reviewer go above and beyond the call of duty.
The real check on fabrication is replication, which usually happen after publication.