Does beats studio 3 has transparency mode?

Yes, but only when you use them in wired mode. Simply hold down on the Beats button and your music will momentarily pause and the ANC will temporarily be disabled. Release the button and the music and the cancelling is re-enabled, however the music will have skipped forward the length of time you held the button for. Alternatively, you can disable ANC in wireless mode by double tapping the power button. Double tap again to re-activate.

This also works in wireless more by double tapping the power button, however it is not the same as transparency mode in other headphones, which bring in sound from outside using the microphones. This feature simply disables noise cancelling, and it is still relatively difficult to hear what's going on around you. Interestingly enough, transparency mode would be possible on this set of headphones, as it activates a similar mode when you make a phone call through the headphones, Apple simply does not offer support for it on their devices as a separate setting like on the new beats solo pro

Yes, if you tap the power button it will cancel the music and turn on "transparency mode" for about 3 seconds before playing the music again.