Q about profile settings

 
I'm trying to understand how I can default/set run profile settings
upon profile creation.

If profile creation happens through the UI, then the Settings class is
instantiated and the Customizer Panel is shown, so I can default there
- but how do I get a Project lookup from the Context so I can find good
values to default things to?

If profile creation doesn't happen through the UI, but through adding
a nature to the project, I still want to pull some things (like 
the default server) into the profile.  Where is there a hook where I can do 
this?

--George