What is your explore team?

[Lyya]

No, it does not affect drop quality or rate.

PC/Steam: New Version (mini update) 2.0.106

No - traitstone droprate was once affected by difficulty (pre 1.0.9 I think, where it was 70% + 5% per difficulty level), but we bumped it up to 100% on all difficulty levels a while back. The quality of the traitstone has never been affected by difficulty.