I notice you are in Thailand at present.
I'm wondering if you are confusing sitting cross-legged (e.g. sitting on a chair with one leg crossed over the other) with sitting on the floor in a "lotus" position (as used in Yoga, Budhism etc), as Thais very regularly do (but which might cause me serious personal injury!).
As a NES, I might "fold my arms" but would not normally talk about folding my legs.
On the second point, I personally have no problem with "leading an exploration" (or more likely an expedition).
Hope this helps
Student or Learner