In the book “Nonabelian algebraic topology: filtered spaces, crossed complexes, cubical homotopy groupoids” by R. Brown, P.J. Higgins and R. Sivera, EMS Tracts in Mathematics vol 15 (2011), Chapter 16 on “Future Directions?” has 32 problems arising out of the previous material, and suggesting areas for development. A pdf of the book is available from the above link. A slightly edited version of Chapter 16 is available as a pdf here.
An earlier paper in this area is R. Brown, “Some problems in non-Abelian homotopical and homological algebra”, Homotopy theory and related topics, Proceedings Kinosaki, 1988, ed. M. Mimura, Springer Lecture Notes in Math., 1418 (1990) 105-129, and a version updated in 2001 is available here.
Another resource is a Bibliography on the Nonabelian Tensor Product of Groups; this has 152 items (with my name on 7 of them).