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Minecraft uses StateMapperBase#getPropertyString to build the property strings uses as variants in blockstates files, but this is client-only. You can take a look at NBTUtil.readBlockState and NBTUtil.writeBlockState to see how Minecraft reads blockstates from and writes them to NBT; you could apply similar logic to generate/parse a state string in a config file. Edit: There's also CommandBase.convertArgToBlockState, used by commands to parse blockstates from strings. This is probably exactly what you want.

If you use three separate properties for the coordinates, you'll need to use fully-specified variants in the blockstates file; like in the standard Vanilla format (e.g. "x=0,y=0,z=0": { ... }). If you use a single property, you can use Forge-style variants (e.g."position": { "0": { ... }, "1": { ... }, ... }). Each { ... } represents a single variant, where you can set the model, texture, rotation, etc. I don't know what you mean by this. Block#getActualState just has to read the values from the TileEntity and return an IBlockState with the appropriate property values set, it shouldn't be storing anything in the TileEntity.

You can have 27 (or more) states in a single Block if you store them somewhere other than the metadata, just override Block#getActualState to return the state based on information stored in a TileEntity or derived from the world (e.g. how many blocks are adjacent to this one and where they are in relation to it). You can tell each element of a model which part of a texture to render with the "uv" property (see the wiki for more details), but this would require making 27 individual models with different UV coordinates. If all the blocks are the same shape (or some of them are), you can make a single model and specify a different texture file for each state using Forge's blockstates format. You could probably mess around with dynamically-generated models or textures, but I think this is the simplest way to do it.

An example would be as follows: https://github.com/CJMinecraft01/BitOfEverything/blob/master/src/main/java/cjminecraft/bitofeverything/container/ContainerFurnaceGenerator.java#L64-L92