How? You aren't casting them, and Rooftop Storm doesn't even try to change that fact. Nor do you get a chance to cast anything between the draw and discard, no matter what the cost would be.
608.2f If an effect gives a player the option to pay mana, they may activate mana abilities before taking that action. If an effect specifically instructs or allows a player to cast a spell during resolution, they do so by following the steps in rules 601.2a–i, except no player receives priority after it’s cast. That spell becomes the topmost object on the stack, and the currently resolving
spell or ability continues to resolve, which may include casting other spells this way. No other spells can normally be cast and no other abilities can normally be activated during resolution.
2. When the commander attacks does opponent get the life total also down?
Yes (unless it's something like Skithiryx, the Blight Dragon). Nothing has happened to interfere with rule 120.3.
120.3. Damage may have one or more of the following results, depending on whether the recipient of the damage is a player or permanent, the characteristics of the damage’s source, and the characteristics of the damage’s recipient (if it’s a permanent).
120.3a Damage dealt to a player by a source without infect causes that player to lose that much life.
120.3b Damage dealt to a player by a source with infect causes that source’s controller to give the player that many poison counters.
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Why bother with mere rulings when so many answers can be found in the Rules?
1. For varina lich Queen first ability if I have Rooftop Storm can I play the cards instead of discarding them?
2. When the commander attacks does opponent get the life total also down? Or do they just keep track of the commander damage?
How? You aren't casting them, and Rooftop Storm doesn't even try to change that fact. Nor do you get a chance to cast anything between the draw and discard, no matter what the cost would be.
Yes (unless it's something like Skithiryx, the Blight Dragon). Nothing has happened to interfere with rule 120.3.
So, no, it doesn't allow you to cast a card you're expected to discard.
A Commander still acts as a regular creature: if it deals damage, blood gets spilled.
RULES OF MAGIC :
http://magic.wizards.com/en/game-info/gameplay/rules-and-formats/rules