Need guidance on selecting proper Gates belt drive components for my belt-ready frame I have a very cheap, locally made bike with a belt drive installed on it (the frame is belt-ready). One more thing to note is that the bike is equipped with SG-3C41 IGH from Shimano. 

The problem is it's cheap for a reason - all stock belt drive components are some kind of Chinese cheap copies, and they perform quite bad (belt itself tends to fall-off often, and local bike workshops weren't able to solve this for me).

I would like to swap both sprockets and the belt itself for a brand new Gates belt drive set - while not changing anything else on this bike, if possible. But I'm getting completely lost when I try to figure out myself which components I need to order, and what size of the belt I need. So far I only figured that I need CDX line of components, and that SG-3C41 should be supported by some of them. I'm totally lost when it comes to details, and afraid I'll buy something that won't fit, as it's quite expensive.

Unfortunately, I'm living in a backward Eastern Europe country, and bike movement isn't very developed here. When I asked for help in a few local bike workshops, they said they don't have enough experience with belt drive either, and certainly are not able to help me acquiring them, as nobody imports those in here. They can only help with installing them, if I'll somehow buy them myself.

I'm ready to provide any exact measurements or additional details, if anybody is willing to help.
The Gates CDX system is supposed to be a bit better than the CDN, but they share the same belt and sprocket design. I believe the rear sprockets are interchangeable. CDC is a different design without the center guide.

You want the 3-lobe sprocket to fit on a Nexus SG-3C41 hub. Videos of how to install these are readily findable on the Web.

Without knowing what crank you have it's hard to give specific guidance. You need to know the bolt pattern and bolt center diameter (BCD) of your crank to find the right front sprocket.  

The trick with Gates belt drives is that they are pretty sensitive to alignment of the front and rear sprockets. You need to know the chainline of the hub and sprocket and make the front sprocket on the crank match that. )Poor alignment may be why your current setup keeps throwing the belt.) If you have a square taper bottom bracket and crank you can adjust chainline by getting a different bottom bracket with a different axle length.