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Identify downsteam segment names, cummulative distance, and left-right side intersect

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I have a feature class of streams as lines. Each stream has a unique name, the end nodes and start nodes are correctly located, and the end nodes of tributaries are snapped to other downstream line segments.

For each tributary, I would like to:

1. Find the name of the steam it pours into and populate the attribute table with that name.
2. Determine and populate whether the tributary intersects its downhill counterpart from the left or right side of the line.
3. Calculate the total length of the tributary from headwater to the sea.

I have good Python skill and could brute force the issue but I am interested in more creative solutions.
I am using Advance (ArcInfo) and 10.1
Thanks for any replies.

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