Regarding your phone turning off at random, look into your settings. Select Display, then tap the Brightness menu item. On the popup, make sure the Automatically Adjust Brightness box is NOT checked. When we first worked with Android phones, we noticed that sometimes the screens would practically turn off for no reason and not respond when we tapped them. It turns out that the light sensor was being very stupid and as a result the screen was essentially non-responsive and gave the impression of the phone turning off. Obviously this isn't the case if you're actually seeing it power down, but it's an option to pursue.
Another thing to consider would be Googling each of your Android App companies to make sure other users of those apps aren't having your problems. Some apps didn't take the Froyo upgrade very well and started causing compatibility issues. I think Android disables these Apps when that happens, but I haven't worked with your phone in particular, so it could be different.
Finally, and this is obvious but bears mentioning, check for software updates with your phone. Android updates outside of the tasty named ones do happen and it's possible that your phone might have some setting that forces it to reboot when it updates automatically. I don't think this is the case, but a 15 second check might solve the problem.
Beyond that, yeah, take it back to the store and get it replaced. You should be able to copy any files on it to a microSD card (if they aren't there already) and make the transition fairly smoothly.
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Another thing to consider would be Googling each of your Android App companies to make sure other users of those apps aren't having your problems. Some apps didn't take the Froyo upgrade very well and started causing compatibility issues. I think Android disables these Apps when that happens, but I haven't worked with your phone in particular, so it could be different.
Finally, and this is obvious but bears mentioning, check for software updates with your phone. Android updates outside of the tasty named ones do happen and it's possible that your phone might have some setting that forces it to reboot when it updates automatically. I don't think this is the case, but a 15 second check might solve the problem.
Beyond that, yeah, take it back to the store and get it replaced. You should be able to copy any files on it to a microSD card (if they aren't there already) and make the transition fairly smoothly.