What does it mean when the controller uses the word "request"?
In civil aviation the ICAO standard phraseology should be used. This phraseology is described in ICAO document 9432. 
The standard ICAO phraseology is to use the word report in the first case.
According to the definitions it means: "Pass me the following information ..."


  [callsign] report heading


The second phrase is even stranger. QNE is the standard pressure altimetry setting of 1013.25 Hectopascal (29.92 inches of mercury in the US). When an altimeter is set to standard pressure, the normal way of reporting the altitude is in Flight Levels. So in this case the standard phraseology should have been


  [callsign] report Flight Level.