Can different-level elements be integrated and overlaid in numerical weather prediction displays, such as combining the 500 hPa pressure field with the 800 hPa or other lower-level wind and humidity fields, and displaying all three on a single chart?

That's a great question. Indeed, meteorological fields (pressure, wind, humidity, temperature, etc.) are frequently modeled at different levels of the atmosphere. In principle, graphs with various fields at different levels provide a comprehensive perspective, such as observing low pressure at 500 hPa and high humidity at 800 hPa, suggesting beneficial rains.