u already answered it by yourself la..

in a simpler way, BOV is used to release unwanted compressed air when the throttle plate is closed (when you lift of the gas pedal).

Wastegate is used to maintain the amount of exhaust force needed to spin the turbine so that the boost is maintained. For example, you set the boost to 0.5bar. When the boost come in, the wastegate will release the excessive exhaust gas so that the boost stay at 0.5bar.

If no wastegate (if la..) the turbine will keep on spinning and the compressor will keep on sucking more air. This is dangerous as the engine may not be able to take up so much of air and the engine might blown into pieces..

and how it works together?

actually, it should be:
BOV is our nose while the wastegate is our A$$

But its a good thing that he asks first than straight transplant. Later kena con by mechanic, habis lor.. hahaha..

If my physics knowledge is correct, narrowing the pipe would make the sound more louder with high pitch/note. While widening the pipe would make the sound with low pitch/note i.e more growl.

Dont take my words for granted. I am not any engine tuner or have driven any turbocharged cars. Just my little knowledge that I want to share..

it should be because of the throttle plate is still open thus, no return pressure for the BOV to release. When the throttle plate is closed, there will be return pressure so that the BOV will be activated.

5uperMan, no need to use BOV la.. its too common already.