Hi TJF2019,
As for the o2 sensor, you most likely only have one. I found a diagram for the F-series which is the same as your except a van body rather than a truck (at least for this purpose they are the same) and it shows one location past the y pipe prior to the converter. The other is for super duty and others so if you only see one on your exhaust, I would not see any reason this is not correct. Also, the main reason is, this vehicle ran fine before with the way it is, so I wouldn't think it is an issue.
As for your issue of not being able to communicate with the PCM this is most likely a wiring issue especially if this happened a while ago and your vehicle still ran find. It could be an issue with the PCM and the data link but I wouldn't think the running rough and not being able to communicate is directly connected. However, if the tech traced the wires, I would assume they are ok but without more detail about what he actually did, we cannot rule it out.
As for your rough running condition. Pulling codes would really cut this down but here is what it sounds like to me. The fact that it runs ok after you disconnect the battery then starts running poorly actually points away from a module. The vehicle runs in what is called open loop when it starts. This means the PCM only looks at a couple sensors to determine air/fuel mixture. Usually this is just the engine and ambient/intake temp sensor and maybe MAP and baro. All the rest, such as o2 sensor are being ignored and it is running off of pre-programmed parameters.
Once it warms up based on engine coolant temp sensor it starts looking at the o2 sensor and seeing how it is doing in managing air/fuel ratio and starts adjusting accordingly.
Barring injectors just hanging open which is unlikely because this wouldn't be intermittent, I think you have an issue with MAF or possibly MAP. A scan tool hooked up can tell us this but without that option, we may need to test it off the vehicle, here is a procedure to clean it (link attached). Then a video on how to test it.
If you get those readings and let me know what you have we can go from there. Just make sure you monitor the voltage and see it nice and steady as you increase RPM and decrease RPM. Note your starting point at idle and then you max point and RPM if you can and if it the voltage jumped at all or reversed direction.
Just to explain the MAF, it tells the PCM how much air is coming in so that it can control the fuel to try and achieve 14.7:1 air/fuel ratio. There is a document attached that will basically say the same thing. However, if this is reading incorrectly, or telling the PCM that there is more air coming in then actually is, then it will load up with fuel to match that amount of air in order to achieve 14.7:1 air/fuel.
https://www.2carpros.com/articles/mass-air-flow-service
https://youtu.be/a6eaOd3ihiE
Images (Click to make bigger)
Wednesday, April 17th, 2019 AT 4:37 PM