Antifreeze leak coming from the red area.
What is the silver pipe part called? Or, the part number
for silver pipe?

 

If it the hose itself, God have mercy on you Ok not that bad maybe, but the other end is connected to the water outlet, below where the upper radiator hose connects and is a BIATCH to get to. I did mine wihile doing the clutch with the motor lowered and tilted and it was still a PITA. I will get you the parts info here in a sec

 

Got to Majestic Honda to look up the parts. Then search for Water Valve. That will get you the listing of all the parts you see there and you can pick the one you need.
Water Valve for 2001 Honda S2000 | Majestic Honda Automotive Parts

That is for an AP1 so update it if yours is an AP2

Are you 100% sure it is coming from that line? Can you see coolant on the line or hose? Or is it just coming from that general area? Mine was leaking from the water outlet itself, and it was the oring. It is a pain to do so if you have to deal with that I would consider doing the upper radiator hose while in there. If it is coming from the water outlet, it will be under the water pump section

Water Pump for 2001 Honda S2000 | Majestic Honda Automotive Parts

 

I had taken off the hose (around the red outlined area) on a previous occasion and noticed that the silver pipe went from a "O" shape and tapered to an oval shape.
I opened the oval shape up a little (with some pliers) without confirming if that was how the silver pipe was intentionally made. When I put my finger under the
area where the hose connects to the silver pipe I saw antifreeze on my finger. I collapsed the silver pipe back to an oval shape again and reattached the hose.
I hope that resolves the issue.

 

Really appreciate the part number for the silver pipe so that I can determine if the
part is intentionally supposed to be tapered to an oval shape.
Thanks in advance.

 

I just put mine back together from doing clutch and some of those lines. That metal line should be round and I do not think the clamp would hold consistent pressure otherwise. If it has been bent and rebent I doubt it would ever seal right again unless you got it perfectly round. On the plus side, that tube is a LOT easier to replace than the line connecting to it And given that metal line is not likely to fail, you could even get one through A Solutions auto parts used for pretty cheap if they have it