At what altitude stalagmite/stalactite caves are located? What kind of rocks are needed to form them?
The classic text has long been "Karst Hydrology and Physical Speleology" by Alfred Bogli, - which I highly recommend.

Karstic dissolution and precipitation (to form stalactites, helictites, etc.) are basically hydrologic processes in which groundwater seeks to attain thermodynamic equilibrium with the carbonate rocks with which it is in contact. Water flows downhill towards the base-level of erosion - generally sea level. But bear in mind that during the last glaciation sea level was about -120 metres compared to modern sea level. To get very high mountain karst the system has to develop and then be lofted by other tectonic processes of uplift. In the Jebel Akhdar of Oman there are caves up to about 2 km elevation, but I guess that some limestone massifs have been elevated higher than that.