I’m a newbie, but since it doesn’t look like anyone explained what is actually wrong with the “heightmap” in the OP, I’ll jump in. What’s wrong with it is that it is not a heightmap. It’s a relief shaded bitmap rendered from a heightmap. The relief shading is produced by choosing a point of origin for the light and then highlighting anything facing that light source. An actual heightmap is usually an array of 16-bit gray scale values giving the height of the terrain at each x,y coordinate on a grid. The typical approach is to have higher values representing higher terrain, with the value 0 at sea level or whatever the base is. Hope this helps.
I didn’t read your entire post, but the issue that happened was that the heightmap I used was poorly made and I just had to use a different heightmap.
To use heightmaps with UE you can use , select the square to want to extract, when press export cloud button and you receive png files fully compatible with UE 4
You wouldn’t happen to know how to properly import from terrain.party to UE4, would you? I can import my heightmap from TP into UE4 ok, but when I do it’s all bunched up and doesn’t look right. I’m pretty sure I need to adjust how big the landscape is in UE4, but I do not know how to accurately do so. There is no kilometer measurement, so I am uncertain. Any help you could provide is welcome.
I am having the same issue as MNRSR.
Getting the map from TP into UE4 is easy, but the results are not good.
Edit: ok dropping the Z down to 30 made a big improvement. I’m now happily sinking in gobs of time into my map. 
Unreal is very picky about the size of a heightmap. You need to use some strange number to get a more pleasing result than the one seen in the screen shots. 512 x 512 belongs, unfortunately, not to these numbers. The next nearest number would be 509 x 509. For a table of possible numbers look at the old documentation for UDK (which was Unreal 3): UDK | LandscapeCreating. terrain.party is a good site for grabbing heightmaps as some one told above but you get some absolutely weird numbers for the size of the heightmap. Also you always have to scale the heightmap down vertically inside Unreal even if the x and y values are set right.
The post above your post was posted 11 months ago. Fyi 
True, but what if other people run into the same problem? The heightmap sizes in UE are strange if you compare them to other engines so it does not hurt to know about the pitfalls with heightmaps in UE.
the terrain.party extractions should go right in, but given the resolution size you would need to simply use UI buttons to adjust fit.
I"ve had similar issues with other heightmaps .
THe largest size you can create is 18KM, as noted on far right side of terrain.party page, and u nderneath there, the ‘-’ icon allows to you decrease that. Pushing on km icon will go back to 18km in whatever increment you wish basically.
Then import and adjust as needed .
I don’t recall how one does that, but that’s the basic idea. ( I"ve not had to yet)
There are many other sources for real data, with opentopgrahphy being another and of course usgs NMV, which is prob. in the end the best way to go, given you can choose whatever size you want ( up to hardware?), and load into WM or (not sure) say PS or gimp blah, and slice up into several 2048 images and bring into world editor in ue4. I"ve not ever tried that as it would be the hard way to go but in theory it should work. Worth testing out, because WM only allows tiled export in the paid PRO version. YMMV
GL
Why not make your own heightmaps with WM and set your own dimensions?
I don’t see the benefit in ripping off of others anyways, if you want to learn might as well go all the way and LEARN.
Edit: If you want to reproduce a real world location, NASA offers quality heightmaps online. I’ve never used them, they may or may not need some tweaking, but I’m sure they’re one of the better sources for that kind of thing. I mean, who could give you a better heightmap of a real world location than NASA?
WM to UE4 Tutorial - UE4 Wiki
A great tutorial on WM to UE4, along with heightmaps it shows you how to create a material for your terrain and offers more insight into what is actually happening - and why you may have previously experienced some issues along the way.
If you get a weird glitch and accidentally fix it, you didnt really learn anything. If you get a weird glitch and try to understand what happened, why, and how it can be prevented, you’ll most likely never experience that issue again, but if you do you’ll know what to do. Hope this can help any future lurkers who stumble across this thread, I know I did when I was having issues with WM to UE4, more specifically, the heighmaps I was exporting from WM were incorrect for UE4 - It was my fault completely. After following this tutorial, it worked perfectly. First. Try.
TerreSculptor also allows for import and conversion of multiple DEM file formats from USGS and other sites for anyone wanting to use DEM files for Landscape.
DEM file formats such as .bil .bt .flt .hgt and others are fully supported. Post back if you have issues importing or use the TerreSculptor forums for questions.
TerreSculptor also has a built in UDK Landscape sizing and resampling selection dialog so that you can get the optimal size heightmaps for use with UDK.
You don’t have to remember any odd numbers or anything, just select from the list on the dialog for what size you want.
If you are working with heightmaps up to the size of 2048x2048 you can download the Standard Edition which is free for all use.
Note for any previous TerreSculptor users that the website and forums and blog have all moved to the new domain.