AHA blew all of it's oil out of the bottom of the engine

[Chris Talley]

Well the AHA managed to blow all of it's oil of the bottom of the engine,
and I need some feedback.

It had been relatively cold in the Pacific Northwest for a few days ( 0
degrees with the windchill). I was warming up the car this morning without
any problems and I go to leave, rev the engine a little and the engine
sounds like it has no oil in the crankcase and the oil light is comes on.

I take a peek under the car and there is oil pouring out from the splash
pan. I pulled the splash pan to investigate and it sure seemed to me that
the source of the leak was the oil cooler/ block interface. There was some
evidence that there may have been a small leak in this area for some time.
My hypothesis is that the seal is broken but I am interested in others
experience and opinions.

My hopefully not completely stupid questions are;

Is it likely my assessment is correct?
Is there a way to test the hypothesis without removing the oil cooler and
using a bunch of oil, and or damaging the engine?
Is it wise/ acceptable to replace only the seal?
Should anything else be replaced while I am in there?
I am correct in thinking there is a thermostat and bypass for the oil
cooler and it is not feed with oil until a certain temperature is achieved?

Thank you, Chris