You can safely use the main preamp outs to your headphone amp. And you can safely use the tape outs without anything connected to the main output.
Personally I would use the main output to a headphone amp. The tape output is almost certainly "buffered" and is not going to give you a better signal than the main out. Even though the main out is via the volume control!
As for the use/non-use of some of the tubes via the tape out, that is up to a manufacturer's design. If the pre has zero gain via the tape out, with the CD player connected, then, no gain is being produced, and perhaps the line tube gain stage is inactive (and only the phono tubes are actively engaged). If the tape out produces a louder signal than direct from the CD player out, then the pre does still have a gain stage in the circuit. (probably, this is not a certainty, as the impedance may be affecting things)
Personally I would use the main output to a headphone amp. The tape output is almost certainly "buffered" and is not going to give you a better signal than the main out. Even though the main out is via the volume control!
As for the use/non-use of some of the tubes via the tape out, that is up to a manufacturer's design. If the pre has zero gain via the tape out, with the CD player connected, then, no gain is being produced, and perhaps the line tube gain stage is inactive (and only the phono tubes are actively engaged). If the tape out produces a louder signal than direct from the CD player out, then the pre does still have a gain stage in the circuit. (probably, this is not a certainty, as the impedance may be affecting things)

