Inspired by the film and this file: http://www.thingiverse.com/thing:2235934

I decided to start learning the fundamentals of Fusion 360 (and added some Blender work too) and create the box from scratch. Apologies for inaccuracies, I'm new to this.

I printed the result too small on a cheap Prusa clone that's been printing almost 24/7 for over 12 months. In truth, it needs some attention, but still produces a reasonable print.

Prusa

Prusa Clone

Doesn't Matter

Yes

Up to 0.2mm

I used 50% as it was a small model. Scaled up you could reduce this much lower I would think.

The Groot itself is prone to breaking at smaller sizes, particular arms and fingers, scale up for better strength. Walls I set at 1.2mm.

Fusion 360 and Blender for the cables and more organic stuff.