The rules for advancing state that a unit cannot shoot after advancing, but the assault weapon rules override the rule on advancing.

Can you fire pistols after advancing?

Rules as written I don't think you can advance and fire pistols, as shooting after advancing only applies to assault weapons. But if did a regular move and then used the strat then you would be able to fire you blasters and pistols. The same would apply if you were in melee.

Can you advance and shoot?

Advance: Models move up to M+D6". Cannot move within Engagement Range of enemy models. Units that Advance cannot shoot or charge this turn. ... Units that are within Engagement Range of any enemy models can only either Fall Back or Remain Stationary.