Is the Audio Technica AT835b compatible with the Sony HC-40? Do any of you know if there is an XLR adapter for the HC-40? Also, do any of you know what the best Sony microphone is?

The AT835b (medium shotgun, XLR jack) will need the right adapter to be compatible for your Sony HC-40 (consumer camera, minijack mic input probably). Your camera should have a mic jack unless it's one of the lowest Sony models which are typically watered down. EDIT: I checked, your camera does have a mic input.

The XLR adapter you need would have to do the following things:
1- give the right volume/voltage level to your camera
2- block the mic plug's power (there need to be a capacitor in the adapter to do this)
3- Not mix the two signals from the XLR together.
4- (not related to the cable) The mic itself needs to be powered off battery. The cable can/will/does not carry phantom power.
5- (duh) have the right physical connectors.

The Beachtek adapter boxes (or similar) will do the job for roughly $200. They mount under the camera.

You probably do not want to use this microphone for your camera as it is very big.

Also, do any of you know what the best Sony microphone is?
Do you mean "what's the best microphone for my camera that works?"

If so, what's your budget?
And I assume you will place the microphone on top of the camera (nearly always the worst place to put the microphone, but acceptable for family videos and such).

Is there a way that you can record sound from the AT835b seperately, like directly on to the mic and then mix it with video in post?

Also, do you know of any good microphones that don't have to connect to the camera and can record audio seperate from it?

Is there a way that you can record sound from the AT835b seperately, like directly on to the mic and then mix it with video in post?

Also, do you know of any good microphones that don't have to connect to the camera and can record audio seperate from it?

You could record audio seperate from your camcorder (referred to sometimes as "double system"), which would add extra hassle to your production and possibly give your better sound (if the recorder is the 'bottleneck') and can give you more inputs at once. For your use it may make a lot more sense to record audio into your camera.

To record audio seperate from your camcorder you need another device that records audio, such as a mini-disc recorder, a mp3/flash recorder (i.e. iriver), laptop with audio interface, DAT, nagra, hard drive / DVD recorder, another camera, etc.

2- What are you trying to do?
3- What is your budget?

If you could answer #2 and #3 the folks here could give you much better advice.

Frankly, I don't think you want to be using the Audio Technica 835b.