How do you record the audio (what you say & hear) from a gamer headset

So, this tutorial has a review of recording devices, including ones that support HD recording. It does note the following

I WILL BE LISTING SOME HD COMPATIBLE RECORDING DEVICES that enable you to record in standard and play in High Def simultaneously later in this article. However the prices can vary dramatically on these devices. There is only one somewhat affordable external device that allows true HD capture and that is the Hauppauge HD PVR and it is listed below.

It also says

As far as I know there are no affordable external devices that record 1080p or from an HDMI cable. The Hauppauge will do HD but it will only record in 720p or 1080i.

Mind you, this guide was posted 3 years ago so there is no guarantee that the devices haven't improved since then, but this seems to be a very complete guide.

Honestly, I think you're going to find better support on the GameDev side of things. A lot of players record their videos (especially those in MLG) but a lot of the times they won't care about audio syncing, or perfect framerates. You can take a look at this guide over at the MLG forums, but a lot of their focus is on cheap rather than quality.

On your PS3 Go to Accessory Settings -> Audio Device Settings. You'll find options for microphone volume there. Try adjusting it to the highest level. Also make sure the Input device is set to Wireless Headset (and not, for example, the USB camera). Make sure you confirm your settings by choosing OK, not by exiting pressing O.

Also, I recommend doing the HQ sync for the headset, to do so, plug a USB cable directly into the headset (not into the headset dock). When you'll trun on or off the headset or adjust the volume, you should see the HQ indicator in the top right corner, it looks like this:

For everything else, I suggest you read the manual, available here or contact Sony's support.