You only need your Pass Cover Number to book Eurostar. This is available with paper passes, but with a mobile pass you need to use the online convertor with the pass number in your e-mail.
You do not need to activate your pass until the day of departure, once you are sure you will be travelling.
Everything else such as adding panned trains to your trip, which is simply a diary of planned journeys, or checking things on the planner can be done without activating your pass, but it will need linking to your trip.
There is no connection between reservations and pass, mobile or paper.
Put simply your pass is active when you activate it on the app or fill in the first day on a paper pass.
You are required to hold a valid, active pass for all journeys and appropriate reservations for any train requiring reservations.
The link to search for and book passholder reservations on Eurostar is here https://www.b-europe.com/EN/Booking/Pass#TravelWish
use with pass cover generator linked above for mobile pass.
I just checked and, at least normal Eurostar bookings, can be made 330 days in advance.
Has pass availabile date changed - It was 180 days compared with retail tickets available from (I assume) the 330 days.
I know last year because I had a requirement for Easter week and pre-bought two retail tickets well before Interrail pass availability (of 180 days) for not much more than current IR reservation fee, just to be sure.