There is no real hard limit - as long as you've got a spell card in hand, and a slot in the S/T zone for it to go, then you can activate it.
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No, there isn't. Unless you count a Field Spell Card, which is a spell card but has its own zone, so technically you can have 6 spells active.
Quick-play Spell cards are Spell Speed 2, so are the same speed as all Trap cards except for Counter Trap cards which are Spell Speed 3.
there is no such a code... sucks
No, it doesn't end the battle phase.
you have to beat the game you have to beat the game