Trading View: how to use the fields from invite-only indicator, inside of my custom pine-script study?

You can use another indicator as an input source.

data = input(title="Data", type=input.source, defval=close)

In the Data input dropdown, you should see the names of the plots of the invite-only indicator.
From there on, you can use that value in an alert.
For details, see How to code an input option for TradingView's ‘apply indicator on indicator’ feature?