I have a Trane BWD724A100A1 heat pump system servicing my 600 s.f.
apartment. The original Weathertron stat appeared to be inop in that
whenever heat is called for the aux heat blue light indicates. I purchased
a Honeywell TH8320U and outside temp indicator that I appeared to wire
correctly to this stat that I just installed. Now, a few ?s:

In the installer setup, should I set the compressor and/or aux heat
lockouts? If so, to what temps? I am in NYC area if that matters.

Is there much of an energy-use difference between using the compressor or
aux heat?

On occasion, after the new stat reaches the set temp during heat cycle, the
"heat on" indicator will turn off but the vents will continue to blow out
air, at decreasing temp. I put a thermometer in the ceiling duct and at
times this air continues to blow out for 20 - 30 mins going down to 63 F
which of course lowers the room temp, causing the heat to have to turn on
again. Even if I remove the stat from the wall plate the vents continue to
push out this cold air for at least several more minutes. As I said, this
only happens sometimes. Sometimes it appears to work correctly and the
ducts shut down shortly after the 'heat on' indicator turns off. How can I
stop this from happening?

Is there somewhere that I can see the correct Installer setup settings for
this configuration?