the output values of "PTAC DX CLG ELEC HTG:Zone Packaged Terminal Air Conditioner Total Cooling Energy J" and "PTAC DX CLG ELEC HTG:Zone Packaged Terminal Air Conditioner Total Heating Energy J" are just always there (without both being zero) . How do I design it so that the system Heating turns off above 20C and Cooling turns off below 24C?

The Always On Discrete hvac_library is name of the Schedule:

Schedule:Constant,Always On Discrete hvac_library,OnOff hvac_library,1;

Those reports are telling you that the air blowing into the zone has some energy content. The supply air temperature with respect to the zone (Tsupply - Tzone) will be non-zero even when the coils are off. Look at the coil electricity rate to see if those components are on. If you don't want the fan to run all the time change the Supply Air Fan Operating Mode Schedule to 0 so the fan can cycle with the coils. Or if you want cycling fan at night and constant fan during occupied hours, change the Supply Air Fan Operating Mode Schedule accordingly.

is there no way to tell them
"run when above 20C"?

when I changed Schedule:Constant,Always On Discrete hvac_library,OnOff hvac_library,1; this to zero to turn off, it gave me fatal error :(. Is there a way for it to turn on only on appropriate/desired temperature range?