The log shows a Facebook certificate error. I thought I recall something about this recently... but I don't recall exact details. sorry. Do you have a church network security device that might be interfering?
Also- Antivirus, in the above log, shows on (not off).
Beware using Wifi... unless you are a network engineer with experience in real-time RF utilization monitoring, you are just asking for trouble. I know if can be a challenge, but during lockdown, I literally ran a 100ft ethernet cable into the Sanctuary for livestreaming Sunday services (we've since upgraded our setup).
Can Wifi work? Yes, but it can easily not work and you won't know if WiFi or something else is the cause. ie, it may appear a random issue (it won't be random, but you won't see the cause, so it will appear that way) There are ways to use WiFi with a higher level of confidence, but it takes the right setup (which most people have neither the equipment nor knowledge to setup & maintain). With consumer WiFi gear, and being forced to use WiFi to stream, I'd be inclined to (assuming being able to livestream takes precedence over other WiFi clients/usage scenarios).
first - disable ALL guest and other client WiFi usage (seriously... nothing but streaming PC allowed to connect) but assuming that isn't practical.
- Put streaming computer on 5GHz Wifi by itself, put all other clients on 2.4GHz band
And that old CPU should work, if careful with Operating System and OBS Studio Optimization, with lower expectations on settings (I'd try 1080p30 before dropping down to 720p). But, that without care, you can easily overwhelm that computer with real-time video compositing. Especially as it appears that GPU doesn't support NVENC (encoding offload... not sure, auto config testing appears to be using the CPU... meaning you are going to have to be VERY careful... then again, looks like that GPU is supposed to have NVENC?? so maybe auto-config wizard simply hadn't gotten that far??)
As for that certificate error - I'll let you search this forum for that issue.
I'd make sure PC Operating System updated, then reboot, let system settle down, then within browser connect to facebook.com/live/producer and try to log in. Can you or are you getting errors? if you are getting errors, resolve them first before starting OBS Studio and trying anything there