[HKS PWR]

1) First things first, determine if there is circulation of water in the zones. If the zone valve is open the water should go through that loop and come by via the return, which should also be warm/hot. If there is no circulation it would mainly be the circulator (pump) and/or air lock (more common on the upper floors). Try bleeding/flushing each loop to get rid of the air.
2) Won't be the outdoor reset because a) this older navien combi boiler didn't have outdoor reset and b) outdoor reset doesn't stop making hot water for hydronic heating. The whole point of the outdoor reset is that it changes the heating curve (for example if it was -10c outside, it would produce water at 140f for in-floor heating. If it was 10c outside, it would probably make it at 100f to save energy)
3) I'm not sure if that Honeywell circulator (pump) has it, put the Grundfos circulators has a removable cover on the housing that cover the shaft. You can remove it and see if the shaft is spinning without disassembling the circulator (be careful since these are wet rotor circulator meaning some water will leak out). FYI chances are if the circulator is seized and not spinning, the housing of the circulator would be too hot to touch.
4) That "T-junction" that you're asking about is "correct". It's one of the ways to pipe these high-efficiency boilers with multiple circulators for hydraulic separation. I say "correct" because it's technically not configured correctly, but still kind of does the job.
5) These older Navien combi boilers do not produce output for both domestic hot water usage and space heating at the same time. The 3-way valve prevents that and will prioritize domestic hot water production, meaning if someone is using domestic hot water, it will not make hot water for space heating.
6) Should really call a heating tech. Good luck getting one to show up right now since everyone turned their heating system on for the first time this week and found out it does not.