Is it possible to record audio from just one application on windows?

Yes it's possible using a software.

You can use a small software called Virtual Audio Cable. http://software.muzychenko.net/eng/vac.htm

After installation, it will create a new sound card with a playback on you real sound card. Then by "cheating". You choose the virtual sound card by default then you launch your application. Then choose your real sound card again and you will be able to record from the virtual sound card and listen from your real sound card.

Put every application you want to record on the virtual sound card and it's ok.

Of course in your recording software be careful to choose the right sound card.

This is possible, but it depends on the software and the sound card.

Sound cards can have multiple inputs/outputs and will allow signals to be routed. Therefore it is possible, if the software allows it, for you to select what output to use. At this point, you can route the signal.

So, based upon the likelyhood of the software giving you this option (which is minimal if not designed to allow this), coupled with an on-board sound card, I'd say no.

I know you can change the volume of all applications independently using the mixer inbuilt to windows

There is your answer isn't it. Mute sounds from all other applications except the one you want to hear/record

This basically requires recording audio from a process instead of system wide audio. It was not possible until now.

A normal recording software will records system wide audio, this is achieved by calling Windows WSAPI API loopback device. This will includes all audio source that active at that time.

Recently a company called D3DGear has developed a technology to record audio just from one process, it will not include background audios from other process. You can check D3DGear to see details of their audio technologies.