What happens if I play reasoning and a monster like BLS-EOTB is the first card to turn up? Is he sent to the graveyard and I stop picking up cards? Is he sent to the graveyard and I keep picking up cards?

he is sent to the graveyard, you stop picking up cards. you stop playing BLS and make a normal warrior deck. You send all your money and possessions to "agent mage's hypnotized realms goers" care of.......

Oh I'm sorry, was I rambling again?

You will stop picking up cards and, even if he's NOT the same level as the level called, he will be sent to the graveyard because he is unable to be special summoned through any card except its own (for the initial summon). The only way you'll be able to special summon him afterwards is to return him to your hand and remove a Light and Dark monster to special summon it.