Hey man, I imported your model here in Unreal to check it out and found some things.
Neat character 
When I imported the model it was rotated and the pivot apparently was on the center of the character.
I fixed it in Unreal but you will almost always want the pivot between your characters legs (especially in bipeds) before you even rig / skin / animate anything. It helps a LOT having the pivot in the correct place, prevents errors and other stuff
You should check/search on blender in their export sections, I know you can change the scale/units you want to export, as well as what is considered the Up axis, I think blender’s and unreal’s axis are different.
(I mainly used 3DMax and we had to rotate the character’s pivot so that the Y axis was up when we were working with Unity3d, but I am not familiar with blender and Unreal so you will have to test it out for yourself)
Weird Lines: When you imported, Unreal surely showed you some alerts saying something along the lines of “vertex X has no weight, setting it to root” or something like that. This is the engine telling you that a vertice is not being influenced by any bone of your character so it automatically weights it to the root, That is why there are those weird lines. Those are vertices that aren’t influenced by any bone when the model was exported and then they were weighted to the root bone by the engine, they were pulled out of position. Check your skin in blender and you’ll see the problem.
I think the main problem you are having is with your bone structure + pivot. The root apparently is on the left of the character. Usually the biped setup used is:
You put the root in the same place as the pivot (between the character’s leg) then it goes up to the pelvis and from there it splits into thights and a spline and from there arms / neck / other stuff
In your setup when I’m looking at the bone hierarchy the radioman has it’s center to the left of the character, then the root is almost at his left elbow. This is really weird.
I’d tell you to remove your skeleton completely change the character’s pivot so that it’s between his legs and rotate it so that when you import it in unreal you don’t have to mess around with rotations and positions, >>>POSITION YOUR CHARACTER AT THE POSITION 0 0 0, IT’S VERY IMPORTANT<<< then you set up your new skeleton with the root at the same place as the pivot.
It prevents a shitton of problems and it’s probably what’s been screwing with you
Hope it helps man, any more questions, just send them away.
