Your pictures of the barrel you made are very impressive and I applaud both your ambition and skill! The artistry it takes to cut, shape, curve, and toast wood so it will hold liquid is not easy to acquire. Bravo to you. To answer your question, it’s possible that some iron filings (from grinding the chime, or the part around which the head fits) are being rinsed out. However, I suspect that it’s coming from a much simpler and harmless source, the wood itself.
In your pictures (below) it looks like you toasted the staves and/or the inside of the barrel itself while assembled. If this is so, it’s only natural that residual charred dust from the staves would come out in the water. Similarly, since wood is porous, it makes sense that over time any water inside the barrel would become darker. Think about making a cup of tea with a tea bag. Dip the bag into the water for five seconds and the water might turn a light barely-brown. Leave the tea bag to steep in the water for five minutes and the water will be much, much darker.
It is entirely normal for the first soaking of a barrel to produce a dark-colored water. This will definitely depend on the porosity of your wood as well as the level of toast on the wood. It will also very much depend on how much, if at all, the barrel had ever been rinsed or steamed before. Just don’t soak that barrel in too much water! Part of storing wine in a barrel, after all, is to soak up the tannins as well as the aromatic and flavor compounds the wood and the toasting process have to offer.