It's possible to use "saber strike" with dying lunge?

No, Saber Strike is a special action that includes an attack. Dying Lunge just grants an attack, therefore you cannot perform a special action.

See above. When a non-hero figure gets to "perform an attack" (for example the standard Attack action), it is performed with the attack type and attack dice found in the figure's deployment (or companion) card. In the campaign, a hero who has equipped more than one weapon chooses which weapon to use for the attack when the attack is declared.