Hi Dragos,
There are many posts on the forums about the limitations of armatures that I am sure you have read. For the most part the way things look at frame 0 is how they will look V3D. When I have scaling issues I reset scale = 1 for all objects and armatures. (Blender: Apply>Scale).
So for your morph targets…if they are not coming in at the same size as the original object…make sure they have all the same scale at frame 0. Then if you are scaling your main object via puzzles, you may want to scale your target(s) accordingly.
Armatures as stated earlier have many limitations and issues. You could use the V3D Bake Armature Action export function but just keyframing your animation has proven to be the most successful if you have complex rigging.
Since your armature is not exporting you may want to diagnose why.
I would export just the rig and start a new project with one simple object parented to the chain and see if it imports… then if not, delete constraints, try again, delete IK, delete one bone at a time and try again…until you find out what is causing the actual issue. Simple chains work. There are known issues complex rigging and without seeing your project I can only guess at potential things for you to try.
Also you may want to open the V3D App Manager in Chrome using developer mode and watch the Console to see what errors its throwing. it might give a hint as to why your armature is not loading.