Re Q2,

MR0374131 (51 #10331) Reviewed
Hironaka, Heisuke
Triangulations of algebraic sets. Algebraic geometry (Proc. Sympos. Pure Math., Vol. 29,
Humboldt State Univ., Arcata, Calif., 1974), pp. 165–185. Amer. Math. Soc., Providence, R.I., 1975.
14B99 (32B20 57C15)

In case you are wondering: no, this does not use resolution of singularities. Hironaka's point in writing the article was to demonstrate that resolution is unnecessary for triangulation.