1. Can this load the tmx files externally?
I am not sure what this means, but if you mean outside of the Unity 'Assets' file structure then yes.
2. Can the png files for the tile sets load externally?
I am not sure what you are asking here either, but if you mean outside of the Unity 'Assets' file structure this is outside of the scope of Tiled To Unity but I am certain there is a way. The texture is just data.
Tiled to Unity doesn't necessarily have to use the same png you use for your tiles. In fact, typically the models you use as tiles have their own textures/uv's etc. If you watch the tutorial videos you will see that in my example the tile sheet asset png is simply a representation of the 3D assets.
3. Can this load the files during runtime?
4. If I need support for coding it into my game will you be able to support it?
Of course I will help you if you get stuck.
The coding involved is the easy part of Tiled To Unity anyway. All you have to do is yourTileLoader.loadTMX("yourFileName.tmx"). It's more work setting up your tiles and tile prefabs.