I am not familiar with skydome, but the marks showing are the polygons of the mesh used for the water.
Could be one of the settings like "Specular Strength", try lowering it, see if it goes away.
Also under your surfaces check that "Smooth" is turned on.

Sorry, I don't remember. It's been awhile since I did anything in Unreal, but from the image it looks like the exported models rootnode is above the character rather than the hip like it should be.

AutoDesk has a free .fbx converter which can help correct some export issuses, you can download it here...

http://usa.autodesk.com/adsk/servlet/pc/item?siteID=123112&id=22694909

Try viewing the model and animations and convert to a newer fbx version with the tool first.
Also this forum is great when it comes to finding answers to Unreal... https://forums.epicgames.com/forum.php

Sorry I could be more help, good luck!

I like it! good work!

If I remember correctly, the problem is the selection for the models IK rootnode in Unreal, try selecting a different ik point as the models root.