300.1. A turn consists of five phases, in this order: beginning, precombat main, combat, postcombat main, and end. Each of these phases takes place every turn, even if nothing happens during the phase. The beginning, combat, and end phases are further broken down into steps, which proceed in order.
300.3. When a phase ends (but not a step), any unused mana left in a player’s mana pool is lost. That player loses 1 life for each one mana lost this way. This is called mana burn. Mana burn is loss of life, not damage, so it can’t be prevented or altered by effects that affect damage. This game action doesn’t use the stack. (See rule 406, “Mana Abilities.”)
301. Beginning Phase
301.1. The beginning phase consists of three steps, in this order: untap, upkeep, and draw.
So, basically, when your Draw step ends, your beginning Phase also ends and you must empty your mana pool.
And for question 1, no you can't they are separate steps, even thought in the same phase.