Heater core recommendation needed + another HVAC issue

[Matt B]

I just got back from feeding the beast at a local gas station and realized that my heater core is most likely leaky. Symptoms are fog build up at the windshield after stopping the engine and moisture in passenger footwell. So... Seems obvious, no?

Rockauto offers a variety of cores. Can anyone recommend any of these? Or are they all the same cheap Chinese crap?

Second issue I have is with the HVAC. Here I found 2 symptoms. First: sometimes, usually upon starting the car, the system sort of "resets" itself to 24 degree celsius, all automatic mode and in few cases also turns on the rear window defogger. Last weekend this happened while I was driving with the system turned off (targa roof was off, so no airflow needed).
Second: with the system in "Off" mode under hard acceleration (not sure if that is relevant) the fan started blowing full power, outlet air was maximum hot. As I don't expect an emergency engine cool down function I suppose my HVAC controller module (??) has an issue.

No LED lights are flashing, no codes present either. What do you think?