Skullclamp & Disciple - Trigger Abilities Question

Player A has 2 card left in library.
Player A has one Disciple in play.
Player B has 1 life remaining.
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Question #1
Player A double clamps frogmite.
Player A must then declare the order in which the 2 card drawing triggered abilities and the disciple damage abilities go on the stack.

So player A must declare that abilities go on the stack in this order:
Draw 2 Cards(1),
Draw2 Cards(2),
Disciple Dmg to Player B.

Then the stack is resolved FILO and Player B would take lethal damage and the game would be over.

Is this correct??

Question #2
If the triggered abilities were played in the wrong order such as; Disciple Dmg to Player B, Draw 2 Cards(1), Draw 2 Cards(2). Resolve FILO. Then Player A would lose the game due to not being able to draw a car from there library.

Is this correct??

Or do I have this totaly wrong?
Thanks
SimpleHiker