1995 was the last year of OBD1. 1996 is OBDII. It would be simplest to just say the exact year that it is.

My first guess would be that the replacement sensor is not the proper one for the car. Is it a direct plug in one or a generic type where the wires have to be spliced?

Also a code 1 can potentially be caused by other factors like fuel pressure making the engine run rich or lean. If the mixture can't be brought into range, all the ECU has to go on is that something is wrong with the "oxygen content" readings it is getting from the sensor. It can't directly conclude that the sensor itself is faulty. In practice people call code 1 the "oxygen sensor" code since it usually is the sensor. The sensors wear out but the rest of the system is seldom a problem. If you have the sensor heater codes, that is more certainly something with the sensor or the wiring.

Checking the harness is simple enough, there are only 4 wires involved. Start by testing that the sensor ground wire has continuity to ground and the sensor output wire is not shorted to ground. Do those tests with the sensor cold, connecting an ohmmeter to a hot oxygen sensor can damage the sensor. Check that power is applied to one heater wire (black and yellow I think) when the key is on. Check that the ECU pulls the other heater wire to near ground when the engine is started. Check for voltage from the sensor on the white wire, it should go up close to 1 volt. Finally check that the white wire is actually connected to the ECU.

 

^ Yup.

I would say that a knowledgeable person wouldn't even need ANY scan tool to be able to diagnose an OBDII Civic. I use a paperclip jumper to pull CEL codes, a CEL code chart from the service manual or this forum, and a multi-meter. I'm no pro, and I don't use any $300 multi-meter. Just use some sense and learn to use a multi-meter.

One code my '00 Civic was throwing was for the primary O2 sensor, but the sensor and harness tested fine. I noticed a small crack in my exhaust manifold by the O2 sensor though, so I patched it and pulled the 7.5A fuse to reset the ECU. Problem solved, until I could source a new manifold at a good price.

AN OBDI vehicle typically has even fewer sensors.

Even the best scan tools will only get you "close" sometimes. You have to use your own judgement and testing to find the real culprit behind something like an O2 sensor fault.