Hi you can't book directly in the app, if link to the Interrail website. 

Reservations and the app are not linked together. 

The app works like a diary where you add all you trips to your pass to get your ticket (QR-Code), on some trains you need a reservation on top of it.

Ok thank you. So can I reserve all the tickets in the interrail website?
I checked on the website and some of the trains seem to be sold out 

If you want advice, let us know the route, date and departure time. It is strange that trains are sold out for this summer. Except night trains which can sell out months in advance

Interrail can't book all seat reservations, mainly in Spain.

There are extra fees too on the website, it's recommended to avoid it. See :

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

https://community.eurail.com/train-connections-reservations-47/how-to-get-reservations-105

Hi, I’ve already read this two links. One thing that I don’t understand is that if I book a train ticket in the official website, I’ll pay the whole prize. So what’s the point to have bought the interrail pass? 
I have also another question: I’ll do the trip in summer, so do I have to book seat reservations for all the routes? If yes, can I make these reservation from the interrail website or are there other ways? 

There usually is a way to only pay the seat reservations on the official websites. For example on tickets.oebb.at : you add Interrail/Eurail as a discount and select one-way tickets.

Seat reservations are mandatory on high-speed trains in France, Italy, Spain + some cross-border routes so yes you need to make them. Eurostar and Thalys can sell out weeks in advance (quota). All other countries mainly have optional reservations which can be a good idea on busy mainlines (but you can make them last-minute).

To avoid interrail.eu (extra fees) precisely use the pages I linked.