Okay, Prereqs are pretty easy to meet, +7 BAB and own a dancing weapon, simple, straightforward, and accessible by anyone willing to wait a few levels.
Skills are... a little odd but I can see the reasons behind them.
HD is fine as is, trade some endurance to be able to fight with a sword from a distance, I like it.
Chassis is as expected, good Fort is common among warriors, and the Ref I can see from wielding weapons this way, good BAB is essential for a warrior.
Wpn/Arm Prof is a good addition, boosts some of the classes that enter.
Bonded weapon is not listed on the table, the Table refers to Extended Dance, is that a carry over that was missed? As for the feature itself, it looks good, a total of 10 extra rounds by the end of the class will make it useful in most combats, unless it's an all out war, that should be sufficient
Echoed Blade is a good way to allow the dancer to melee at the same time and would just look awesome on the field. And the ability to let it dance as well is a good one, limiting it to one round makes it a little less useful but for good reason.
Freed Blade, adds a little distance, keeps the weapon close, and gives some bonus options when fighting, looks good, not overpowered, but useful nonetheless.
Forced Opening is a good option for a Dancer, makes sense thematically and has good combat effects if you work as part of a larger unit, esspecially if you have a rogue or similar class in the party
Living weapon is an interesting ability and definitely a good capstone, it removes the normal limitations of the dancing quality and directly upgrades it, which is essentially what the class is about.
Dancing Weapon Tricks:
Spoiler
Show
Two Weapon Dancing, keyed towards the Ranger, obviously, but also good for a fighter or TWFing rogue, good option overall if you can afford it. Only question is if Echoed Blade works on both simultaneously
Weapon Call is a perfect way to give back actions to the dancer, very good overall option for them regardless of how they actually fight.
Dancing (Maneuver) Tricks: Good for fighters with a specific fighting style or for anyone else with the feats, and a good way to use them while still being able to attack more directly.
Extra Bond seems like a more general version of Two Weapon Dancing. A better option for more focused single weapon fighters
Dancing Defense is a good choice for lightly armored warriors and rogues, I'd take it myself since I like my defenses. How would this interact with Two Weapon Defense and Two Weapon Dancing?
Dancing Reflexes has such a good image to it in my head, and the feat it provides is useful.
The Playing a Dancer of Blades part provides good advice for anyone that wants to take the class, which is always nice
Overall, I think it's well balanced and nicely done.