If the caller is on favorite list then it rings.
Yes. If the caller is a favorite, it will ring no matter if Do Not Disturb is on.
That depends on the settings set up for DND. It's possible to set it up so that no calls ring.
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I have it on whil iPhone is locked. However incoming call still Rong where it's suppose be silenced. Is this a bug?
Have you checked your DND settings to see how call handling is set up there? It's possible, for example, to allow various groups to still call, or to have repeated calls come through.
Have you made sure that DND was in fact enabled?
If you only have it set to working while the phone is locked, was the phone in fact locked when the call came in?