Understood, but it means if I want to see the content of a folder and/or subfolder (like Sent, Trash or any other I created), I have to do it manually, right, no automatic synchronisation of folders and subfolders ?
No, you don't need to synchronize these other folders manually. The app provides a "schedule sync" which will automatically update any changes that occurred on server side (delete, move to another folder, reply, star/unstar, read/unread, etc.) available on device (client) side, and also the other way around
Scheduled sync is a scheduled process (event based and/or time based).
To summarize:
Scheduled sync is scheduled sync for
all folders.
Push is an additionally thing for
selected folders. Push means that there is a permanent connection to the server, so the server can push the new mail immediately to you. And you will get a notification about this new message.
Example:
If your inbox folder is enabled for push, then every new message will arrive immediately and independently from scheduled sync.
However, scheduled sync will also work for the inbox folder, though. To 'catch' any change (e.g. read, star, delete,...) that occurred on server side.