The pictures help..... yes, you have only one processor and one heatsink. The heatsink, from the picture showing the label clearly on the side, is the version that ends with -002. That is the one to get.... both it and the -001 versions have the higher cooling capacity and the one that ends with -003 has 2 instead of 3 heat pipes. You also can use the heatsinks off the xw6600 and xw8600 (the single height ones) just fine on the xw8400 for this processor.... have done that.
You want two of those SLAEJ versions from eBay. They are so darn cheap now...... The heatsink also is cheap. Remember to update the BIOS first even before doing anything else.
Dust.... I have an air compressor and can clean these up in about 5 minutes. Get a bamboo skewer so when you are blowing into each fan (including into the power supply from front and back) you don't over-RPM them. And don't blow on the internal speaker because you can rupture it.
Note the HP plastic cover protecting the second processor socket's internal pins..... those are very delicate. You can read up in the forum on how to be very careful while you set in the new processors. It is all in here, and use the search box at top left of this page because it targets this forum only. It is pretty easy to do.
Yes to getting two of the SLAEJ processors rather than one. Your xw8400 is near dog slow right now. It is using the next to slowest dual core, and with the SLAEJ processors you'll have quad cores and nearly the fastest ones certified for that workstation. There are faster ones you could try, listed in the latest QuickSpecs for the xw8400, but I have not tried those and don't know if they will cause the fan RPMs to rise from what is a nice quiet workstation with two SLAEJ processors in place. Your choice on that.... still cheap.
Make sure to get the 300GB version of the Intel 320 series SSD... those are inexpensive and work great. HP has cautioned to use SATA generation II drives in these workstations, and I know others have not followed that guidance with SSDs in these but I've never had an issue with the Intel SSD advised above, ever, and have seen and heard of issues with using SATA generation III drives in them. So, I'm not taking any risks with my builds or my advice.
Finally, if the xw8400 is running W7Pro64 right now you want to harvest its COA serial number so you can re-enter than when you do a clean OS install on the SSD. There are little utilities that let you do that. Those never came from HP with W7, and you do want to start with the W7Pro64 version.
There are optimized BIOS settings I can send you if you PM me via the forum and learn about Replicated Setup in BIOS. I can email you the little CPQSETUP.TXT file that lets you clone in my settings.