For reentry the Space Shuttles lowered their perigee to 28 nautical miles (52 km) above sea level. Shuttle Columbia disintegrated around 60 km altitude, and the first debris fell off as high as 70.5 km. Given the fact that the perigee didn't intersect the Earth, could some debris have made one or two more orbits around the planet?
No. Even the highest ballistic coefficient debris (engine turbopumps, etc) only made it to Louisiana.
Heavier objects with higher ballistic coefficients, a measure of how far objects will travel in the air, landed toward the end of the debris trail in western Louisiana.
Source: CAIB Report Volume 1 p. 45 & 47
Unlikely. From the Wikipedia page on orbital decay:
Due to atmospheric drag, the lowest altitude above the Earth at which an object in a circular orbit can complete at least one full revolution without propulsion is approximately 150 km (93 mi) while the lowest perigee of an elliptical revolution is approximately 90 km (56 mi).
70.5 km is well below that. On that same page there is a link to an open-source software package that allows you to simulate orbital decay, if you are interested to model this further (I have not used the software myself).