No, no delay when snapping pics. That was one of my biggest must haves as I have a young child that is always on the move. I've been very happy with this camera. No problems with the battery life. I did buy extra batteries though so I always have an extra one ready to go.
No delay on snapping pics if you turn off the review. Some settings may have a little. I am happy with the battery life. I snapped about 200 pics with flash at a 3 hour reception and still had battery life left to take plenty of nature pics on a hike the next day.
Battery life is fair, I'd say. I bought a couple of extras and keep them charged and handy, especially when out and about. Hard to quantify the delay question, focusing can take a moment or fail completely in certain situations. One can minimize the problem by prefocusing and then tripping the shutter at the desired moment.
There is a little delay. More on some settings than others. I would say the battery life is good but I would recommend having a backup. I haven't had the camera for long and I'm no expert so I don't know what would be considered normal usage. I have shot over a hundred pictures on one battery and that is with some playing around with the camera also. Hope this helps.
About delay when snapping photos - I don't see any since you have to adjust focus when you press half way down to focus for each shot. The manual says you can keep snapping away and the camera will catch up. If you want a faster camera you'll have to go to something more professional and more expensive. Battery life - The Canon Battery that came with it doesn't last that long. I went on Amazon and bought the Wasabi 3.7V and ultra high 1300mAh with their charger and they last a long time.