1998 v6 Temp sensor & Temp switch problems, need help please

Hi, I'm new to this forum. My poor horsey mobile has the check engine light on. I took it to oreily and the diagnostics scan said, "P0125 Insufficient coolant temp for closed loop fuel control." My horsey mobile has a bad history with it's antifreeze system cause the last owner was dumb and put just water in it. It even needed to have a pump replaced because it was all rusted out. My temperature gauge has never worked right; it doesn't move from C unless I've been driving for a while.
I bought a temperature sensor from Oreily's and put it in the spot next to the intake manifold, screwed into that brown metal pipe, where only one wire appears to go into it. Now, the engine light's still on and the temperature gauge actually moves farther left towards "C" than when the car is off. I think I also need to replace something called the "Temperature sensor switch" or something. It's another 20 dollar part I'm getting mailed in from oreilys, but I don't know where it is to replace.
Also, I'm afraid I might have them mixed up or something. The sensor I took out was (rusty) and looked like a cylinder shape on the end, where as the one I put in was cone shaped like this one: http://www.latemodelrestoration.com...5-Ford-Mustang-50L-Coolant-Temperature-Sensor .

1. Did I put the right sensor in? Or does it just look newer.
2. Where's the other temperature thing. Is it this one near by with the two wires?
3. Are those two brown rusted pipes I'm showing you replaceable? Is it practical?
Thank you for any advice.

After the water pump was installed, they flushed the coolant system and burped the system. When I took out the sensor today, I noticed there was antifreeze in there, so it's definitely making contact with the fluid.

It was flushed a while ago. I'm just now putting the new sensors in. I haven't gotten the other one yet so I won't be able to tell if they're working right just yet. My check engine light's still on, and I'm afraid if the sensor's don't work right, they won't turn on the fan when the engine does get hot.

OK so the sensor I put in wasn't the right one. In fact, I'm thinking the one I put in goes in the second spot. It doesn't have any notches, so it fits into either of the plugs which made it confusing. I bought a second sensor today, which has a cylinder shaped tip, and put it in the spot on the right, and the temp gauge actually works!(after about five minutes of running.) I still think my car's leaking somewhere though...