Downspout drain lines.

How much slope, minimum that is, do I need for a downspout drain?

How are these sized? I have one drain (neighbors actually but it's 5ft from my house, and I asked permission) that is 3" picking up maybe a 400 sq ft area and a 26 sq ft area I'd like to add mine to it that is picking up maybe an additional 50sq ft. Ok?

What about adding a catch basin too? Not much water really except for if the hose is leaking or gets left on or something. Would also allow for a relief point should it back up or have too much flow.

Thanks,
Jason

google a website for a vendor of product...like NDS ( National Diversified Services) and they may have charts for drainage on a sq.ft. vs rainfall basis.