<p>If someone creates a 3D model of a character for 3D printing can I import that model into Unreal engine or Unity 3D for use in a video game? Also is the inverse true? Can I get 3D model of Mario and send that to a 3D printer?</p>
<p>Specifically, it’s more important to know if I can pull a 3D printer model into an unreal game project</p>

I haven't seen lifts that aren't on the edge of the print, such as warping, or the entire printed surface lifts.  When I get something like in your photograph, it's because the print surface isn't flat and the first layer matches the surface topology.  If the second image shows the print surface, it looks like blobs on the surface that may be keeping it from being flat.
The first layer thickness greatly depends on how high the nozzle is above the print surface.  If this distance varies, the first layer thickness will vary.  Also make sure your print surface is free of any substances that the hot extruded material might cause to boil.
Any chance you are removing the print from the bed before it cools down.  This can distort the print if the material is still soft.