A:Answer 1) Front Speakers
These are likely component speakers, meaning the tweeters and woofers are separate, with the tweeters either in the upper part of the door or in the dash. Make sure to confirm and buy the correct speakers.
2) Back Speakers
These are coaxial speakers (the tweeter and woofer all in one), so just swap them out.
3) Do you need an amp for these speakers?
No, you can just hook them up to the existing wires that run to the stock stereo system. You should experience a material improvement in quality sound. The stock stereo of the 2009 Sonata has an output of 80 watts, so likely up to 20 watts per speaker. The speakers will be greatly u def powered from their potential, but will still sound good. You'll likely do well to get even a small amp like a Kicker 202.4 that may fit behind your stereo and even run off the 12v cable that runs to the stereo. Your other option is to upgrade your stereo too.
If I were you I'd just swap the speakers myself and see how they sound. Then, if you want even more power, I'd buy and I stall the small Kicker 202.4 amp, only making it power just the front speakers (tweeter 1, tweeter 2, woofer 1, and woofer 2.) You'd get up to 50 watts per speaker (for each front tweeter and each front woofer.)
I just installed these speakers, upgrading the stereo with a 10" touch screen Jensen, the Alpine S speakers, and the Kicker 202.4 amp. The enhanced sound quality and increased loudness is awesome!
Start small with just the speakers and see if that's enough.
Good luck!