Can't tell much about HIK. However, you can click the empty black area in HIK panel, which will select all the controls, then set Reach IK T/R to 1.0; some controls will also require partial or full Pinning (now, except the ankle ctrls, where you can see those two Ts: unpinned):

Now it is manageable, however, I still can't tell why it all should be enabled, because, I believe, you should be able to work in FK too; yet it snaps back, idk.
Now, you still have skinning wrong, e.g. - the left part of face is affected by the right shoulder, the upper jaw by spine; when the leg is raised, the jacket's lower part self-penetrates, and so on.. The eye controls most likely also need to be constrained to some head joint.
To solve self-penetration, you have to have identical topology on both flap sides.. I just tried to add edge loop on the inside and deleted Non-deformer history, and it had no effect on overall rig, the blendshapes still work. Now, either paint in Replace mode some exact values (you can use PSWTool color-picker) on its both sides OR open ComponentEditor and select vertices in pairs and enter values until those are identical; locking some of influences might make it easier. Also, you have MaintainMaxInfluences in Skincluster enabled.. I would consider disabling it, because it can screw up all the scrupulous things done on one influence in favor of the next influence I am about to edit; happened so many times, a f*kup-setting, unless you have some game engine limits/budget. Also, pruneSmallWeights often, and remove/lock the unnecessary influences (fingertips, toes) in skinCluster - the less is more.
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Maya2019.1 @ Windows10 & GeForce GTX1080Ti
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