Hello,
For your first issue: Destiny does not feature a Self-Mute option. This is dependent on the headset you use in game, or console specific apps for voice-chat (E.g. PlayStation Party App)
For the second- If you do not opt in for Team Voice Chat, you will not hear other players in the game, nor will they hear you.
English
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Do the same rules apply to destiny 2 for PvP and PvE matchmaking?