There's a long delay from the time I push the button until the flash goes off and the picture actually takes. I miss the smiling child and get a turned head instead.

Sounds like have inadvertently activated the child lock, select any program and press and hold the start button until the key light goes off approx 5-10secs. If this does not work please repost with model number as with some bosch models it is a different button you need to hold. (may be the time delay)

This is a common situation with almost all point-and-shoot cameras. The delay is because the camera has to do so much when you push the button. Bulkier and more expensive SLRs eliminate the delay by having more hardware to handle the various tasks.

You can reduce the delay by anticipating the action. If you know where the action is going to happen (a child blowing out the candles on a cake, or right in front of a soccer goal, for example) aim the camera there and press the shutter button halfway and hold it there. This meters the exposure and focuses the lens. Then when the action finally happens, press the shutter button the rest of the way. With the camera having done most of the work when you pressed the button halfway, there will be much less delay.

Again, the delay is a basic "feature" of the camera design. It can't be completely eliminated, but by pressing the shutter release halfway it can be reduced.

This is a common situation with compact point&shoot cameras. Between the time you press the shutter release button and it takes a picture, it has a lot to do. It has to find the subject and focus on it, meter the light and set the exposure, perhaps set the white balance, and other things. Larger, more powerful (and more expensive) DSLRs have more powerful processors and additional hardware to speed up the process.

One way you can reduce this shutter lag is to press the shutter release button halfway to focus and meter before you need the picture. Keep the shutter button pressed halfway until the action hits its peak, then press it the rest of the way.

This is a common situation with compact point&shoot cameras. Between the time you press the shutter release button and it takes a picture, it has a lot to do. It has to find the subject and focus on it, meter the light and set the exposure, perhaps set the white balance, and other things. Larger, more powerful (and more expensive) DSLRs have more powerful processors and additional hardware to speed up the process.

One way you can reduce this shutter lag is to press the shutter release button halfway to focus and meter before you need the picture. Keep the shutter button pressed halfway until the action hits its peak, then press it the rest of the way.

If its showing a key symbol then the child lock is on.Press and hold the start/pause button in for several seconds and this should take the child lock off and start to work again.

This is normal behavior for most compact point&shoot cameras, especially one of such vintage. You can eliminate some (though not all) of the delay by pressing the shutter release button halfway to meter and focus, then press the button all the way at the peak moment.

Pre-focus by pressing the shutter button half-way until the camera beeps, then press the rest of the way when the moment is right.

The delay is caused by the flash charging. Put the camera in Program mode (P on your dial). This is similar to Auto, but you can turn off the flash. Press the button with the lightning bolt by it until you see the same icon but with a slash through it in your LCD screen.

Now keep in mind taking pictures this way will often result in blurry pictures because you're overiding both the Autofocus (by pushing all the way down on the shutter instead of first half way), and the flash (you may need to keep the camera extra steady in low light situations).

The flash need to be fully charged before it would fire the shot.

In case the battery is old and supply power is not enough to boost the flash, it will await until the orange LED of flash indicator is no longer blinking, means ready to take picture with flash light.

Replace the new full battery will be better and faster to take shot with flash enable.

Melzim, another user, is exactly right. The lower-end digital cameras experience a significant shutter delay when using the camera; it's an unfortunate fact. 
What you can do, outside of investing in a newer model (which do have improvements over the earlier models) is simply try to anticipate your subject's movement - or concentrate on portraiture, etc. 
There is a huge value, over time, in having pictures of smiling families, standing still, believe it or not. 
The A85 is simply not the camera to use to freeze action.
-lizwb