Why did you use automatic weighting? Makehuman already gets good weighting. It’s missing the twist bones but they would not work with automatic weighting anyway (the left shoulder on your screenshot looks very off… this could usually be fixed easy and quick with a twist bone that just turns a bit backwards).
I don’t know the workflow from Makehuman -> Blender -> UE4-Tool -> UE4. I only know the way Makehuman -> Blender -> UE4. That would be:
*) Export from Makehuman centimeter as dae
*) Import into Blender
*) Import the UE4 mannequin into Blender
*) Pose the Makehuman character to get a (very) similar pose to the UE4 mannequin (afterwards delete the UE4 mannequin)
*) Apply the armature modifier to (all) meshes, apply the pose as new rest pose in pose mode to the skeleton, add armature modifiers back to the meshes.
*) Add twist bones (they are a must have). Copy vertex groups (e.g. upperarm_l) and split the weight up (autonormalizing on and subtract and blur) between the twist and the normal bone.
*) If you like you could add some IK bones. They are pretty useless in UE4 (as you could use the IK functions even without them in UE4) but very handy while animating in Blender.
Regarding the twists at the fingers. It is very, very, very … very… important for retargetting to get a Rest-pose that is similar to the UE4 mannequin in Blender. The rest-pose is the pose that would be used if you switch to edit mode. You could see it even if you click on that little human like button on the right side of blender when you select your armature. There is a pose position button and a rest position button. The rest pose should look like the A-pose of the mannequin. If you get annoyed by a few anims too much you could even just disable the retargetting of your fingers (leave the mapping at the retarget manager empty) before you retarget. Your hands would be in the restpose of your hand afterwards (no twists but even no “grabbing” pose). You could pose your hand in UE4 afterwards apply a key at the first frame and export (and reimport) the anim. It is usually not that difficult (a matter of 1minute per anim) to pose your hand properly from the rest-pose to the “grab some rifle” pose. But it is a pain to untwist all those weird twisted fingers manually. Anyway I would recommend you to fix the rest-pose.
Actually it is possible (just retargetted the same anim from the free anim starter pack (don’t use that anim-set in my game)):
Regarding your “low-poly” question. Forget Makehuman-low-poly for UE4 …except probably for some LOD (much, much later)… or if you go for mobile. If I would be create something for moblie based on MH then this would be a heavy retopo session anyway ;)… and not those low-poly meshes. UE4 renders polys very well. It is more likely that you slow down your game with adding some effects with transparent materials than with too much polys of your main char. If you don’t make a strategy game where you see thousands of them 30-50k for your main characters are very ok.