Question

does formic acid conduct electricity?

Answer 1

YES! formic-acid (HCOOH) in water dissolves into ions (H+ and COOH-). 
since formic acid is a weak acid, the amounts of ions are small. and you know a solution is called electrolyte if it can conduct electricity. and to conduct electricity a solution must have ions. so formic acid is a weak electrolyte (compared to water, for example).

Answer 2

yes , because of the presence of hydrogen ions