Your amp is very weak. You probably want something with more power, especially for classical music. In a good recording quiet parts of a musical piece should sound quiet and loud parts should sound loud. The R70X rewards a good amp and this is something you may want to investigate.
Don't increase the bass or treble if you want it to sound neutral. Few good DACs have bass and treble controls because they tend to lead to undesirable compromises.
It depends on the recording. Classical recordings can vary wildly. Quiet parts of a classical piece will always sound much much quieter than compressed pop music. A lot of pop music is compressed to make the music sound equally loud throughout a song or album. It is common practice to push this loudness as high as possible because many people think loud = good. (
https://en.wikipedia.org/wiki/Loudness_war) You can make your own mind up whether compressed music is desirable or not. To me music you want to listen to seriously should not be compressed but if you want background music that stays at a similar level no matter what, then compressed is good.