okay so looking at your specs you do have an esata 1.5 port.
esata can come in 1.5 and 3.0 speeds, but since your internal sata runs at 1.5 my assumption is that your external sata port will do the same.
as far as compatibility with sata 6gb/s drive to a sata 1.5gb/s, i'm seeing that this drive provides jumper settings to go from 6.0gb/s to 1.5gb/s.
http://wdc.custhelp.com/app/answers/detail/a_id/5387#jumper
notice how its confusing how it says "jumper settings for sata 6.0 gb/s 3.5 hdds"
but at the top it says for both 3.0gb/s hdd and the WD1002FAEX.
my guess is that they chose this size drive to support 1.5gb/s for popularity?
there are other sizes that have 6.0gb/s and what ... do they have to succumb to 3.0gb/s speeds only?
maybe someone else can take a look and see if i'm missing something.
but if i'm right, then yeah this drive should support 1.5gb/s provided that you set the jumper.
"Is it possible to hook up a SATA 3.0 (well SATA 6 with 3.0 backwards) up to the machine through the eSata port?"
well this is a 6.0 drive so it won't work at 3.0 speeds since your esata port is 1.5
it will instead work at the 1.5 speeds when the jumper is set.
there may be another issue... let just assume the drive supports 1.5 and all.
"A single eSATA/USB cable can now power up an eSATA/USB capable device as compared to the original eSATA device which requires an external power source. A notebook can supply up to 5V to power up a 2.5" HDD/SSD, while a desktop can supply up to 12V to power up larger devices like 3.5" HDD/SSD or 5.25" optical drives."
http://en.wikipedia.org/wiki/ESATA/USB
according to wiki, your esata port will only provide 5v which is only enough to power a notebook hard drive 2.5 where as the hard drive your interested in is 3.5 which needs 12v.
it would be possible to hook up a computer power supply to the wall and connect the molex power cable to the hard drive and then connect the drive to your esata port to use.
i just have to ask, why are you wanting to buy a 3.5 internal drive for use on a laptop when you can just get an external usb drive?