Do lava flows on the moon sometimes overlap highlands showing that maria deposits are younger than highlands?

Apollo 16 landed in the Descartes highlands to answer this very question. John Young and Charlie Duke were sent to Descartes to find signs of volcanic lava. They found none. Every rock they brought back was classified as a breccias. Apollo 15 landed close enough to Hadley Rille to sample its material. They found a few grains of volcanic material in samples collected near the rille. The photos they took of the rille and their own observations showed that the rille was a collapsed lava tube. Most lunar geologists believe that the lunar rilles are remnants of ancient lava flows. Although there is also evidence to support the fact that some rilles were formed when the subsurface solidified and the surface above sank to fill in the gaps. Some scientists also believe that some of the rilles formed when the moon cooled very rapidly.

There are some areas of the moon where the maria is older than the highlands, but very little of it. For the most part, the maria is younger than the highlands.

A very good source on this subject is the book "To A Rocky Moon" which can be downloaded as a PDF free from the Lunar Planetary Institute website. the first 17 chapters talk about how the Apollo landing sites were selected. Chapter 18 puts all the information together for you.