I am an S3 user (and now have a dSLR). I agree with the previous folks, especially the parts about the ISO and using a small tripod.
I would try to set up your food pics in a way that gets as much light as possible, without relying on high ISO or flash. Sometimes this is as easy as moving a dish a bit on the table, sitting near a window, or just asking someone to move out of the light for a second. The biggest secret of all is that you must keep the camera perfectly still if you want sharp and no blur.
For fireworks, the same holds true. You have to keep the camera still. You might want to look into a gorillapod which can wrap itself around poles and such. Try using the fireworks setting for ease of use as long as you have a tripod/gorillapod. There is a longer shutter speed so even the slightest movement during that time will cause blur.
I agree with using Aperture Priority if you like bokeh (blurred backgrounds). You can adjust the aperture using the arrows on the back, but it's limited how wide the aperture can go on it. Some of the semi-auto modes will do the same thing, like portrait and night portrait modes.
You have an excellent zoom already, you shouldn't need much more than that in most situations.
There is a really long running thread here for S3/S5 users, you should read through it, you'll get lots of other ideas there.
http://www.disboards.com/showthread.php?t=1235546&referrerid=70088
Good luck, and have fun!
