You don't need to activate your pass to make reservations. In fact, the advice is not to activate in advance at all and wait until your first travel day.

In addition, other websites are often cheaper and more reliable for booking reservations. See this thread:

and this page:

https://www.seat61.com/interrail-and-eurail-reservations.htm

Best only to activate your pass just before travelling. So then you’ll be good with your NEW passport or ID-card number.

Getting reservation without an active pass is very much possible, please see this topic for a full overview on where to get reservations for which train:

Feel free to ask here on the community for advice or help when making seat reservations. Don’t forget to mention exact travel dates, times, trains,… in order to help you the best as possible;

Thank you! This link https://www.b-europe.com/EN/Booking/Pass#TravelWish
which I found on this website you gave me ( https://www.seat61.com/interrail-and-eurail-reservations.htm) is quite useful for Eurostar trains to the UK. However, it seems to me that the Eurostar train is available at any time for holders of an interrail pass. I think I could even book a Eurostar train for tomorrow if I wanted to. This confuses me because I read my times that there are limited seats for interrail travellers on Eurostar trains and that they are sold out quite quickly.
Do you know where I can check the real availability on this website https://www.b-europe.com/EN/Booking/Pass#TravelWish?

B-Europe shows the availability for passholders and the price. 

In doubt let us know your travel date.

I doubt that trains are available tomorrow but it may be possible for evening departures for example.

Tuesday, wednesday and thursday are usually quite okay demand wise for the Eurostar. A late cancellation or rebooking can also lead to more availability.

Other days are much harder to come by. But the advice still counts. As soon as you know on which days you’re taking the Eurostar, you should book it. As it’s on of the few connections where it’s very difficult to find proper alternatives.