Re: The progress bar inside the app, CPU usage and the network traffic caused by the app. But after about 2 or 3 hours it finally stopped and now the problem is gone as the progress bar is now only showing up for a second or two after a new mail arrived.
When using push, the app turns on "sync by X number of days", it's a technical requirement.
And then it's able to do "incremental" sync, getting just changes every time, which is what you want for push.
But:
To get there, to establish a "baseline" for this "incremental", it essentially has to ask the Exchange server to "replay" the creation of every single existing message in your account, folder by folder.
It ignores / skips / rejects the messages that are outside the set date range, but the way Exchange works, this data has to be retrieved and exchanged between the server and the app.
Unfortunately, there is no faster way to establish a "baseline" for "incremental" sync, the way there is for IMAP (for example).
EmClient (Windows mail app), which also uses EWS to connect to Exchange, works the same way, I've seen it in their FAQ.