Will the API allow me to do this ?

Hello,
I don’t know the API yet. I hesitate to create an application.
Will the API allow me to get trade posted not executed that we see on the left when trading a crypto ?
I would like to get this information to assess potential manipulation.

Yes.

If you subscribe to WebSocket Stream <symbol>@depth (docs), you will receive updates every 100 milliseconds with total quantity of outstanding buy and sell orders at every price level. The same information you see when trading on the website.

You can’t access this data at individual order resolution, only an aggregated summary in 100 ms intervals, but that is enough for lots of applications.