When polynomial GI implies polynomial (edge) colored GI?
Q2: a nice example is the graph labeling gadget used to prove that:

Theorem: Planar 3-connected colored GI $\leq_T^L$ planar 3-connected GI

See Thomas Thierauf, Fabian Wagner: The Isomorphism Problem for Planar 3-Connected Graphs Is in Unambiguous Logspace. Theory Comput. Syst. 47(3): 655-673 (2010)

The "labeling gadget" used preserves the 3-connectedness and planarity constraints.