How can I remove the delays in this code for sweeping the servo?
From your code it seems like you are doing all the servo movement before you read the distance and report back. A lot of code is commented out, so it's a bit difficult to follow. What I would do is something along the line of:
[...]
int servoStart=0;
int servoEnd=90;
int servoPos=0;

[...]
void setup() {
    [usual setup stuff like you do it now]
    myServo.write(servoPos);  //start at pos 0
    // Maybe a delay here to make sure we are at pos. 0
}

void loop() {
    //Switch direction if we reach end
    if (servoPos+servoStep &lt; servoStart || servoPos+servoStep &gt; servoEnd)
        servoStep = -servoStep;    
    servoPos += servoStep;
    myServo.write(servoPos);
    //Small delay?
    //Read distance
    //Send distance to seraial
    //Buzz buzzer if needed
}