When I first imported my character into Unreal, it looked very bad — dull and whitewashed compared to Maya. I was disappointed and considered rendering everything in Maya only. But I had some effects planned in Unreal, so I spent a few days fixing lighting and textures until the character looked better.
I exported each shot as a separate FBX with skeletal mesh instead of trying to apply multiple animations to a single skeleton. This solved most of the import problems. Every shot worked correctly after that.
The clothes and the second character posed separate challenges. For the clothes, I imported the Alembic caches and set the time ranges, and it worked. For the other character I downloaded online, FBX import never worked in Unreal, and even Alembic caches gave only one material slot instead of eight. I had to go back to Maya, assign materials individually to each mesh element, triangulate, bake the animation, and then export Alembic. This was a tedious process, but it worked in the end.