Cloth problem

It does work. But it's better when using Mecanim animation, instead of Legacy.  Since Mecanim mirrors the humanoid animation while Legacy flips the model completely, potentially inverting the polygons in the process.

the mecanim bones need a root bone of any kind?

thanks

Yeah, with Mecanim you'll need to adjust some values for the imported animation files.  I find the values listed in this post best.  Have a test and see how it goes, that should resolve the feet and rotation issues.

360 issues are usually due to Quaternion / Euler differences when creating rotations.  Since you're using Blender, this is actually fairly easy to avoid.  Just make sure you set your Transform's Rotation Mode to Euler instead of Quarternion (which I think is default?).

Oh, her knife.  I didn't realise she was an asymmetric character .

Is there any animation applied to the knife, or is it just simply parented to the hand bone (so rotates with the hand, does not animate by itself)?

Then Legacy is the only way to animate it (it won't mirror on 2P side otherwise).

Unfortunately, that means your cloth physics won't work as good now. 

I suggest having a look at Dynamic Bone add-on.  I've had some good success with hair and cloth rigged using it.  You do need a bit of setup to get it working, but it's a nice simple implementation of basic dynamic physics.