I agree with what J. Greathouse is saying, yes, separates would be better if everything else was equal. However, if you are just going to put the separates in crappy places, then it won't really help. It's much better to get the speaker placement right first. I'd rather have fullrange in good placement than separates in areas with poor imaging. If you're just going to put the speakers in the stock location and then put the tweeters somewhere else distant from the midrange, it might sound good, or might not depending on the ones you buy. As usual, just because something sounds good on a sales demo wall doesn't mean it'll sound like that in your car.
Yes, speakers are important. You could put as many amps and better head units if you wanted, but it will still sound bad if you have bad speakers. Concentrate on those first.
Yes, it is still possible to use the factory amp with everything else being aftermarket. If you wante better sound, you just have to spend more money. Dead Link Removed
All frequencies travel through vibration or air movement, it's just that the very low frequencies are more difficult for the ear to localize, especially when the sound waves are so much larger. You should still try and have the midbasses correctly angled as well, because the majority of vocals come from this driver. If you put the tweeters from separates in a good place, but leave the midbass in the stock location, the tweeters may sound too loud, because they're in better positions.
Good luck