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I am unable to ID that. It appears to be a trail of insect feces, or an egg sack, possibly.

If you turn the hose off, nothing can come out, since it is off. It is not an outlet for your house water system, it is part of your water system. All water feeds from your water heater or ground supply and goes to all outlets in your home, including your hose.

Water from all sources in your house go down the drain to a single pipe which feeds to your septic, or sewer lines.

We would not be able to help you coordinate volunteers; that is not a function we provide. Perhaps an ad in a local paper or flyers placed in public places will generate volunteers.

I am only finding causes such as sinusitis, allergies and certain medications. I am not seeing those symptoms listed for plants. Toxic reactions to plants are often vomiting and diarrhea. Of course the allergen plant ragweed causes allergy symptoms that if bad enough or becomes sinusitus could result in loss of taste and smell.
I looked at all the reactions to plants on poison.org and some other sites, but came up empty. You might try checking more sites that list poisonous plants such as the ASPCA.

This article may help you:

https://www.gardeningknowhow.com/ornamental/trees/tgen/tree-stump-removal.htm

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