To 1. The link you cite concerns IKfast. This is just one class of kinematics plugins - it is known to work especially well for 5-7 joints - and does not directly represent "MoveIt" as a whole.
TracIK et. al. do not have such a restriction in the same sense, but I'm not sure how well they perform on higher dof. As the number of singularities increases, they hit problems too.
Our lab currently works on a plugin based on particle optimization that works much better in that regard.
But that's not yet publicly available.
UPDATE: The mentioned plugin can be found here: https://github.com/TAMS-Group/bio_ik
Also keep in mind that "DOF of an arm" refers to joints along one chain. For human-like hands you have a number of (rather short) different chains for the different fingers.
To 2. A part of this question is open research. MoveIt supports you with grasping and esp. deals with obstacle avoidance and path planning aspects for you, but you have to compute the grasps you want to use on your own and provide them as a Grasp message.
Also you need to represent the gripping action somehow. If you want to use the off-the-shelf pick pipeline, this requires you to provide an action server that boils the complex design of your hand down into two numbers saying "how much do you want to close the hand" and (optionally) "how much effort should be applied".
Nobody requires you to make that translation fixed though and it might vary across requests.
-- Clarification --
MoveIt can handle Multi-Chain Robots and you can specify where to move each chain (e.g. "finger" in case of a human-like hand) and plan and execute the motion for the full robot.
Prominently Shadow Robot has a MoveIt configuration for their dexterous hand here.
I'm not sure moveit is appropriate here; I think the topic you're looking for is "grasp planning"