[RPG] Multiple attacks with a dancing weapon

No. From the SRD, Natural Weapons:

Creatures do not receive additional attacks from a high base attack bonus when using natural weapons.

The "Rules of the Game" column is describing the effects of a Druid class feature, which grants Multiattack to animal companions even if they don't have the prerequisites, and grants a bonus attack if they normally have only one attack. The extra attack has nothing to do with BAB and two attacks is all that Druid's wolf can have, regardless of the Druid's level.

For Dancing Weapon: No, dancing occurs in her square. She provokes from enemies adjacent to her,they attack her.

For Greater Dancing Weapon: Yes and OAs are provoked from squares adjacent to the weapon

First, the power of Dancing Weapon:

You release the dancing weapon, and it hovers near you until the end of your next turn or until you drop to 0 hit points or fewer. You can deliver basic attacks and attack powers through the dancing weapon as if you were holding it yourself (including all attack and damage modifiers you'd normally apply). If you do not attack with a dancing weapon before the end of your turn, it makes a basic melee attack against an enemy of your choice within 2 squares of you as if you were wielding it. A dancing weapon cannot make opportunity attacks. Except during brief moments when it is attacking, a dancing weapon remains in your space, even if you move away or are teleported. It automatically resists any attempts by other creatures to take hold of it. At any time during the encounter, you can take hold of the weapon again. This ends the effect.

Sustain Minor. The sword continues to hover and fight near you until the end of your next turn.

The first line we care about is: "You can deliver basic attacks and attack powers through the dancing weapon as if you were holding it yourself (including all attack and damage modifiers you'd normally apply)"

Therefore, it counts as if you're holding it in your space when you use it like a normal weapon. If, as is intended, she activates it, and then pulls out a different weapon, the cool bits of dancing (free MBA) occur.

Second, the power of Greater Dancing Weapon:

Effect: The weapon animates and dances in the air in an unoccupied square adjacent to you. You can use a move action to cause the weapon to fly up to 6 squares to a square that you can see. The object occupies 1 square, and it cannot flank. Its defenses equal 10 + its level, although it cannot be harmed by any attack. If an attack hits the weapon, it returns to your hand (or it falls in your space if you don’t have a hand free or in the nearest square if it can’t reach you), and this power ends. You can use a minor action to end this power if the weapon is adjacent to you, causing the weapon to return to your hand.
While you can see the weapon, you can make weapon attacks with it while it dances, using its square as the origin square of the attacks (including all attack and damage modifiers that you would normally apply).

For this power dancing occurs in the designated square which is used as the originating square for those attacsk. She therefore provokes opportunity attacks from monsters adjacent to the weapon's square. For monsters adjacent to her, she appears as if she's either concentrating or constipated, and does not provoke for that attack. They get to attack the weapon which will send it back to her hands if the OA is successful.