To be clear about your first question, you don't need PA's UCI to link your application on your account.
All you need is the sponsorship application number, which you can find at the top of your AOR email.
When you go to link your application, try application number and family name of the PA as it shows on your AOR letter. Then use either passport info or place of birth. I would recommend passport info.
As for your other question, on ecas it will say
3. We sent "PA name" a letter on "Date". Please consider delays in mail delivery before contacting us.