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At first glance I think you could solve the first part of the problem using Tarboton's 'Upslope dependance function' as this would give you an upslope 'catchment' for every grid cell. This would mean using the Dinf flow direction grid (which less restrictive than D8 (used in ArcHydro) in terms of angular direction of flow). However, this would mean computing it for every cell and for some cells this would be null (top of mountain).
By the second part "downstream distance to a point grid" I assume you mean maximum drainage distance to a cell?
I'm still using version Taudem 3.1 on ArcGIS 9.3.1
Anyway, hope my comments help.
Colin - It looks like the GUI is not written for V10.
I found what I was looking for under Spatial Analyst Tools>Hydrology>Flow Length. I'll still need to do some other work to get what I want, but this what I was basically looking for in the beginning.