I'm on the second land and need to get to the higher ground, so I keep explore the cave that I found with the mist or do I have to do something else?
Keep exploring the Miasma Forest. There's a Mining Node you need to reach to get the item you'll need.
But it says specifically that Pierce/Splash damage weapons won't... is that a text error?
Pierce and Splash are effects: Pierce deals damage to a column, Splash deals damage to adjacent targets. Swords Dance does not work with those two effects on weapons.
My only question is how do I build them? Focus on binds or status effects? Or put a few points in all of them? I feel it is better to max them out since % base and all.
How much should I put in Tame Ground and Bracing Walk?
I had two points in Bracing Walk and it was fine for most the game; basically, just put however many points you feel like you need as you go through the game. Tame Ground is essentially pre-req only fodder.
As for Binds/Status Effects, general suggestion is to max Poison and the Binds and just have base points in the rest. Honestly, an Arcanist alone isn't really enough to keep both Status Effects AND Binds up on a given FoE/Boss fight so binds are generally better there.