besides an SATA cable, where would the power source come from.
eSATA and SATA are not the same connector. (although they work on the same principals). You would need a conversion cable or to just purchase an eSATA hard drive.
Here is a link to an adapter cable (this is just an example, DO NOT PURCHASE THIS PARTICULAR MODEL LoL):
http://www.pcconnectionexpress.com/IPA/Shop/Product/Detail.htm?sku=8114846&cm_mmc=Nextag-_-8114846-_-G2LES3S06W6-_-CI&srccode=cii_9324560&cpncode=17-56592199-2
Almost forgot to answer your second question: Depending on the hard drive they will have either their own power cable that comes with it or it will just run on the eSATA power like some USB HDD's do.
If you computer was made in the last 5 years it should have a SATA connector inside the case and it will be powered by the spare cables that come off of your power supply.
P.S. eSATA is primarily used as an external hard drive format while SATA is internal... both are faster theoretically than current hard drives perform so performance should have nothing to do with your choice.
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