I own the same watch (3820), my second one -- first was stolen, and my experience is that it should not deviate more than +-2-3 seconds/day (depends on the usage pattern). My first one was 100% accurate and my second one, I acquired it pre-owned, is under test because it may require cleaning/oiling soon.
About your questions:
#1) My first guess is that the watch is magnetized and a watch maker can fix this in no time without the need to open the case. Other guesses, in low order of priority, is a "tangled" coil. In any case it pays to have the watch checked using a time machine (my watchmaker uses a Witsch Watch Expert) that can reveals if the watch needs more attention.
#2) This is a more complex question. Since the chronograph of the XX is can level operated (I believe), it's expected a reduction of the amplitude when the chrono is engaged that may interfere with the accuracy but this is not expected on a brand new watch.
If your watch is still under warranty, you should take to a Breguet AD.
Welcome to Breguet,
Nilo