The fan is a high-current device. I am not sure of the specifics of the civic cooling fan of the top of my head, but it is likely a 20 amp draw on startup.
This is a big impact, because most alternators are only 80 amps or so. That means the alternator must instantly induce a 25% increase in output, which will most definitely bog your engine for a second.
As soon as the ECU sees the increased load, it should open up the IAC enough to return the idle to the regular RPM's.
I am not sure if this is what you are describing or not, so please let us know more specifically what you mean by lose power and the revs go up and down.
First of all, wiring up a manual switch is NOT the proper way to fix this, and in my opinion a BAD idea unless you really know what you are doing, which from what you are saying on here, you don't. (no offense intended) If you wanted to wire up the switch for manual control of the fan, it is possible, but again, it must be done correctly. The penalty for doing this wrong is a potential fire or destroyed wiring in your car. The PROPER way to wire up a switch would be to utilize the relay, and use the switch as a 3rd method of providing ground. See the 2nd picture below, the switch would need to be spliced into the GRN wire under-hood and then run into the cabin.
Here are the schematics so you know all the components involved. It has to be one of the things on this list. Use a DMM and figure out which component is faulty instead of just throwing (guessing) which part is bad. +12v refers to battery voltage in this case, which may be more or less than 12v exactly.
The first image refers to the location of the parts in the system. The only parts that are NOT shown are the ignition switch (obviously, where you insert your key) and the underhood fuse box, down by your left foot. There is 1 fuse inside this fuse box.
I will try to break it down for you in case you don't understand how to read the second image.
There are 4 fuses that must NOT be bad for the system to work.
Fuse No. 41 is the main fuse for the whole car, it fuses between the battery's + terminal and the rest of the car's electrics. The car wouldn't run if this was bad.
Fuse No. 42 is the main fuse for the under-dash fuse/relay box. None of the interior electrics would work if this was bad.
Fuse No. 20 is the first fuse of real concern. It provides 20A of power to the "power" side of the fan relay. The "power" side of the fan relay has power all the time.
Fuse No. 17 is the fuse inside the car. It is also of concern here. It gets power whenever the ignition is switched on, which prevents the fan from ever running with the car off. This fuse provides the "control" side of the relay with a switched 12v+ signal whenever the car is on.
You can see that in order to start the engine cooling fan, the "control" side of the relay must be provided a ground. The ground is EITHER provided by the ECM/PCM OR by the ECT switch near the thermostat (behind the distributor, near the VTEC switch, ect) If either of these devices provide a ground, the relay will trigger the fan to turn on.
Check to make sure that each of those fuses is good. DO a visual inspection as well as a resistance check using the DMM. resistance should be zero across all of those fuses.
Next, check to see that the +12v is actually getting to the relay. Pull the relay out of the fusebox and use the DMM to check for voltage. One lead should go to a known ground (such as the neg. terminal on the battery) and then probe the other lead into the terminal sockets. With the ignition set to OFF, only one of the 4 sockets should be getting +12v. This is the power input side. With the ignition set to RUN, 2 of the sockets should be getting +12v. The new socket with voltage is the control input socket.
If these are working, check the relay. Use jumper leads to hook up the control side of the relay to the battery terminals. Im not sure how honda labels their relays, but normally the pins will be 30, 85, 86, and 87. If hondas are different, im sure you can look it up with google. You want to hook up 85 and 86 in this case (the "control" side pins). When you do, the relay should click. Unhooking them should make it click again. You should also hook up the DMM to terminals 30 and 87 (The "power" side pins) and check for resistance. With either or both 85 or 86 unhooked, you should get infinite resistance. With both 85 and 86 hooked up, you should get 0 resistance.
You should check to make sure you were replacing the correct sensor. Try unpluging the ECT plug and jumpering the GRN wire from it to the engine block or any other good ground with the ignition set to the RUN position. This should make the relay trigger (you will feel/hear the click)
If that works, you should unplug the fan connector and ensure that the +12v and ground are getting to the fan properly. With the GRN wire still jumpered to a known good ground, use the DMM between the BLK/RED wire's terminal in the fan connector and a known good engine ground. You should get +12v. Then hook the leads between the ground terminal in the plug and a known good engine ground and check for resistance. You should get zero.
This is about all I know to say to help you. If you are still stumped, please take the car to a certified mechanic so that they can do the repair properly.