[RPG] Does going prone break a grapple

No.

The power's description doesn't explicitly mention the Melee keyword for the sphere's attack, therefore that attack is not a Melee attack.

The only restriction is that the attack's target has to be adjacent to the sphere, but a close blast 1 or a [non-provoking] ranged 1 attack has the same effect. This means that the range restriction cannot be used to guess any implicit keywords of the attack in that way.

Compare the wording of these Conjuration powers, some of which explicitly mention the proxy's attack's type:

Flaming Sphere^[DDI]:

[...] You conjure a Medium flaming sphere that occupies a square within range, and the sphere attacks. [...]

Mordenkainen's Guardian Hound^[DDI]:

[...] You conjure a Medium guardian hound that occupies 1 square within range, and the hound makes the following melee attack. [...]

Ball Lightning^[DDI]:

[...] You conjure a Medium ball of lightning that occupies 1 square within range, and the ball makes the following attack, which is a close burst 1. [...]

There are two different things happening here: your movement speed being halved, and spending half your movement speed. These work differently, and the order matters. The end result is that the grappler can't move-drag after standing up from prone. Here's how it works:

1. You start with your full movement speed.

   Let's use 60′ for the sake of example.

2. Standing up costs half your movement.

   Your current speed is 60′, half of which is 30′. To stand up you spend 30′ of movement. Your speed is still 60′.

3. Dragging while grappling halves your movement speed. Your movement speed this round has now been reduced to exactly how much you've already spent, so you will have 0 feet of movement to spend.

   Your current speed is 60′, but attempting to move-drag a grappled opponent changes it to 30′. You have already spent 30′ of movement and have zero feet left to spend.

The end result is that after standing up, you still have half your movement left, but as soon as you try to drag a grappled opponent you will have no movement left and remain where you are, so realistically you won't bother trying to drag that round. (You could still end the grapple and move your remaining half movement though, of course.)