I will start off by admitting out right that I don't know your camera. It's been a while since I used a non-DSLR so what I say here is based on memory and what I have seen DSLRs doing on auto mode.
Your focus problems are caused by the cameras inability to shoot in low light. This happens on DSLRs too, but you can put fatter lenses with lower f-stops on them which helps a lot (a quick google told me your cam goes from f2.7-4.5 which is not bad when zoomed out, but slows down a bit when zoomed in). They also use phase detection for focus unless used in live view.
Ok, to get back to your cam, it uses contrast detection. This is much slower and less accurate, and why you especially suffer in low light. What the camera does is focus in and out until it can "see" hard lines of contrast. If something is out of focus, it is rather blurry, but in focus it gives a crisp outline. Now, when it's darker (at dawn and dusk for example) it's harder for it to pick out a clear hard line. Even if the subject is in focus, it might be dark on a dark back ground which fools the camera a little.
Your camera should have a few focus modes. If it is set to multi-point mode it's going to pick the object that is closest to you to focus on. This is because the camera was designed with the mass consumer in mind, and the mass consumer wants to take snaps of people without anything between him and his subject. Not the case for wildlife where there are often bushes and twigs in the way. Have a look for a center point AF mode (you mentioned spot focus). This will ignore everything except what is in the middle. Note though, that the area of the center point is often larger than we think so while this is a better bet, it might still focus on something nearer to you if it's kinda almost in the middle of the frame.
Chances are that the exposure metering is linked to your AF point though, so if you set it to center, and then take a pic of something dark like a buffalo, you might end up with an over exposed image. You'll have to give it a go and see how it works out for you. You'll do better darkening a slightly over exposed image in post processing than having an out of focus image though (assuming it's not so over exposed that your whole pic is white).
On DSLRs you can set focus mode to a few different choices. I won't explain them now but assume, based on your description, that your camera is set to only take the pic once it feels it has locked focus. The fact that your camera is hunting in good light means it might need a service, or it's being blinded by something very bright. Afraid I can't give you a solid answer here. Have a look in your manual if you can change the focus mode, and play around again.
The flash response is bad even on high end DSLRs. That's why you can buy external flashes. They are usually worse on lower end models. The flash on your camera works by having a capacitor charged up, that can discharge quickly (much quicker than a battery) and release all the energy needed to make the world bright. The downside is that it takes a while to charge the capacitor. The time you are waiting between shots is what is needed to do this. Afraid there isn't much you can do here. You can try using rechargeable batteries, the lower voltage but higher amperage means the flash will charge faster. But not a major difference. Fresh batteries will probably make a bigger difference.
Hope this helps. It sounds to me though that you have reached the limits of your camera and are being frustrated by it. I suggest you take the plunge and buy a low end DSLR. For me going from a Canon S2 IS p&s to a 500D made a world of difference, and the step up to a 7D again let me get the shots I couldn't before (how many birds in flight have you managed with your Sony?
). Shooting in full manual mode just gives you so much more control and lets you get those crisp, colourful images your crave. On that note, bare in mind that the lenses are the expensive part of the system, so keep that in mind if you start to consider this option.
One last point, go Canon