I'm not sure this will work. Rain garden is a fancy word for a big puddle that slowly sinks in or evaporates. Boggy muddy loving plants are introduced for aesthetic reasons.

This front yard will turn into a soggy mess. A swale, lined and filled with river rock, would be a batter alternative to let the downspout water drain thru the yard and onto the sidewalk. Let the runoff find its own way to the street at that point.

This sounds great! If you are ten feet away from the house, you are golden. Good planning!

Right now, the downspout flows onto the sidewalk anyway, right? So putting in a rain garden will make that situation better. The water has to go somewhere. So the overflow should be fine.

When you do your infiltration test you will find out more that will address tracefloyd's comment above. If your infiltration rate is less than 24 hours, you can plant anything on the list. If it is more, then select the wet-loving plants.

Even those people whose infiltration rate was "never" before teh rain garden, built a fine rain garden where water soaked in quickly. Once you add compost and native plants, the water soaks in much more quickly. Don't worry!

Happy spring!