What is the highest a helicopter can fly?
This (and more) is quite easily answered by Wikipedia

Highest altitude without payload
12,442 m (40,820 ft)
Aerospatiale Lama

Highest level flight altitude
11,010 m (36,120 ft)
Sikorsky CH-54 Tarhe

Altitude with 40-tonne payload
2,255 m (7,398 ft)
Mil V-12

Visit the linked Wikipedia article for more records and sources.