Initially I wanted to make a short tutorial with only a few tips and tricks, but I ended up detailing every step of the way. This was also my first time ever recording technical speech. So it's long. Very. See below (click SHOW MORE) for direct links to specific sections.
0:50 - Mixamo FBX export options (original pose vs. T-pose)
5:02 - Clearing all transforms for a pose (i.e. reset it to rest pose)
5:58 - Semi-automatic symmetrization of the skeleton in Edit mode
7:39 - Semi-automatic symmetrization of the mesh in Edit mode
11:22 - Basic operations on skeleton bones (rotation) in Edit mode:
11:54 - Collective 90° rotation of arm bones around individual origins
13:20 - Collective 180° rotation of leg bones around individual origins
13:49 - Spine adjustment: collective rotation by non-trivial angle
14:29 - Fine rotation adjustment with extreme zoom and dichotomy (neck)
15:15 - Fine rotation adjustment by automatically snapping to cursor (head)
16:33 - Systematic rotation around two axes (thumbs)
17:45 - Rotating bones around the primary axis: by directly entering a roll value
19:35 - Rotating bones around the primary axis: with a set of three regular rotations
21:43 - Adjusting foot bone rotation to align with toe bone and mesh appearance
24:20 - Preliminary look at possible issue with lower leg shape
25:20 - Creating the bone hierarchy for Unreal's foot IK
27:18 - Fixing the legs: constraining foot bones to IK counterparts
29:18 - Translating lowerleg sections with the feet constrained
30:45 - Unconstraining the feet and realigning them to the legs
32:39 - Applying modified pose (lowerleg) as new rest pose
33:59 - Checking/fixing mesh/skeleton symmetry after applying the pose
35:38 - Connecting the leg chain (automatically snapping to cursor)
38:04 - Rotating the clavicles into place (also adjusting their alignment)
39:55 - Review of the Mixamo skeleton after the adjustments
40:56 - On second thought: correcting the alignment of the toe bones
43:40 - Renaming the bones according to the Unreal convention
46:26 - Adjusting the scale of the head and lower body, applying as rest pose
48:21 - Checking/fixing mesh and skeleton symmetry for the new rest pose
50:36 - Normalizing rotation for the armature, rotation and scale for the mesh
51:32 - Deleting the leaf bones (named "*_End") from the armature
52:24 - Importing the UE4 mannequin, first look at bone orientation convention
53:33 - Importing a version of the Mannequin with intuitively reoriented bones
54:45 - Close look at differences in bone orientations: the clavicles
55:29 - Close look at differences in bone_orientation: spine_01
55:58 - Reorienting spine_01 in Edit mode (angle forward by 10°)
56:30 - Clavicle rotation: there's no simple way to rotate around a vertical axis
58:28 - Workaround: rotate the bone into the horizontal plane first
1:00:29 - Superimpose the mannequin to figure out the forward clavicle angle
1:01:39 - Rotate the clavicle forward, using the Mannequin's clavicle as a guide
1:03:37 - Raise the forward-rotated clavicles by 9.5° again
1:04:40 - Preparing to match bone axes orientations to the UE4 mannequin
1:05:10 - Enabling the display of bone axes
1:05:35 - Rotating the bone axes by 90° for the spine (Y backwards, X up)
1:07:13 - Appropriate 90° rotations for the arms (X flowing from right to left)
1:10:49 - Appropriate 90° rotations for the legs (X flowing up one leg and down the other)
1:15:07 - Adding hand IK bones consistent with UE4's Humanoid Rig
1:16:57 - Making IK feet coincide with the real feet in the rest pose (constraints)
1:19:01 - Checking the bone orientations by constraining to the Mannequin's A-pose
1:21:18 - Adjust the scale of the character (match the floor-to-pelvis height of the Mannequin)
1:22:22 - Temporarily normalize the scale of the armature to 1
1:22:45 - Finding the correct scale for the character (0.85) and applying it
1:23:46 - Restoring the meter-to-centimeter scale factor 0.01 for the armature
1:24:42 - Reviewing the character prior to export, saving Blender scene
1:25:44 - Exporting the character and skeleton (textures stored externally)
1:26:51 - Dropping the FBX exported character into Unreal Editor