Does this change the number of cards you are allowed to play in a battle (before/after a die is rolled)?
No, it does not change the number.
Does the 3rd Ed. only allow to play ONE card per side BEFORE the die is rolled and any number of cards AFTER the die is rolled?
Russians are the attacker. They play an Event Card in the Commitment Step. Germans then also play an Event Card.
May the Russians play "Conflicting Hitler Directives (#34 in 3rd Ed. and #15 in 2nd Ed.) to cancel the German's Card BEFORE the die is rolled?
May both sides play another card(s) for the same battle (although they have played a card BEFORE the die roll) AFTER the die is rolled?
For example Germans want a reroll playing "Knight's Cross Wearers" (#16 both Ed.) and Russians then play "Hitler's Interference" (#36 both Ed.) and another "Play anytime"-Card?