Retargeting a Mocap Rig Becomes Upside Down and Weird

I’m new to Blender (coming from Cinema 4D mainly). I can’t figure out how to correctly retarget a mocap rig I got from Mixamo onto a simpler rig.
Before retargeting:



After retargeting:

Using a walking-while-holding-a-gun animation:

(https://i.stack.imgur.com/vD28A.gif)

I would appreciate if someone could help me figure out the following: 1) Why it makes my rig upside down or perpedicular to the mocap animation 2) Why the animation is not correctly followed as seen in the provided GIF
Here is the blender file which I think should help in figuring this out: https://files.fm/u/zxke6d27

Here’s the new file:


Here’s how far I’ve gotten, but something is still wrong.
It’s correlating to the correct parts as if it were rotated 180 degrees, yet the direction of rotation for bones is the same (not rotated 180 degrees). See gif for better explanation: