So my problem is that I'm trying to move the character forward during an attack using "root motion", but the character dont move anywhere. Can somebody spot what I'm missing here?

Heres a link to a video where I show my settings, the problem etc: https://www.youtube.com/watch?v=CWISOsEAj-w

I would like to know what settings should I use in the import and in the move file?

Generally, it's a better idea to avoid Root Motion and instead control your character's movement via Self-Applied Forces.  But if you have a good animation, you may want to use it as you will get the full intended motion the animator has created (like for cinematics).

There are 3 things to make sure Root Motion works:

1) Your character Hitbox Setup needs to have a bodypart hitbox that is assigned to the root of the rig.  If using the Blender Human Meta-Rig, the object "metarig" should be your Root bodypart.  I believe 3DS Max's is "bip", but I'm not 100%.  The rigs in these packs have "motion" object as the Root bodypart.

2) The animation in question needs to have the correct import settings so the Root Motion still takes place.  I've found the following works best:

3) Lastly, in the Move file's Animation options, set Root Motion on and ensure the same Root bodypart assigned in step 1) is used for your Root node.

If these settings don't work for you, then it's possible the animation's root node isn't correctly set up (usually common when you have an animation created separate from the model).  Try assigning the root node in the import settings, under the Motion drop down.

Just to be clear. Should I be able to move the big yellow sphere (character collider or something) using root motion?

EDIT: I assume this because Mistermind has said;
"Move Editor -> Animation -> Animation, toggle Apply Root Motion. This will force the character's real position to move to its motion position during a move. On UFE 1.5 you can also select the Root Motion Node." in this thread: http://www.ufe3d.com/forum/viewtopic.php?pid=2090#p2090

I looked through your videos, and I can't see if your character is set up with a Root bodypart assigned.  If none is assigned, selecting the Root bodypart in your animation's Root Node will do nothing essentially...

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Now, after going back to a project I thought I got Root Motion working in, it turns out this was only for vertical movement anyway (Import settings).  Horizontal movement still required Self-Applied Forces, but this would be OK for simpler movements like where visual foot sliding is easier to avoid.

I was able to get horizontal movement somewhat working by selecting the Root Node in the animation, but then the animation's rotation was off (but at least there was no odd camera snapping when the move finished).  We probably need to extend the root motion function a bit more, so I'll note it down for a future update.