Yes, A caster can have more than one in effect at the same time.
There are no limits to the amount of spells you can have active at any given time unless a spell says otherwise, buffs are subject to stacking penalties, but any spell cast will durate when it reaches the end of its duration.
Yes, A caster can take a double move ( Two move actions ) to control two spheres in one round
You get three actions in a round, a Standard action, a Move action, and a Swift action. A standard action can be used to make two move actions in a round ( A double move ) so that you can control more than one Flaming sphere per round. However doing so gives up your cast for that round.
No, Directing the sphere to move does not provoke an attack of opportunity
Direct or Redirect a Spell
Some spells allow you to redirect the effect to new targets or areas after you cast the spell. Redirecting a spell requires a move action and does not provoke attacks of opportunity or require concentration.
Yes, The sphere deals damage upon entering an enemy space on your initiative count, and it must be moved in a straight line.
The spell states the following:
A burning globe of fire rolls in whichever direction you point and burns those it strikes. It moves 30 feet per round. As part of this movement, it can ascend or jump up to 30 feet to strike a target. If it enters a space with a creature, it stops moving for the round and deals 3d6 points of fire damage to that creature, though a successful Reflex save negates that damage. A flaming sphere rolls over barriers less than 4 feet tall.
Emphasis mine. Since the sphere moves in whichever direction you point, you cannot direct its movement other than pointing to an enemy, which causes the sphere to roll towards said target.
Also, the sphere deals damage when it moves into an enemy's square on your turn, upon which its movement halts. It remains in their square dealing damage if they don't move during their round on your initiative count every turn during its duration. You can choose to move it into the enemy again on your initiative count, upon which it will then cause its damage again.
However it should be noted that Reflex negates, so spell-wise the spell Scorching Ray is a better alternative against enemies that don't have poor reflex saves.