First of all, the comment regarding your intended application is very important. For this answer, I'm going to assume the you want the highest data rate possible (i.e. Wii-type controller that sends near-instantaneous data). I give you two options below. In both cases, the receiver is simple: receiver board (either another XBee or the sister board of the transmitter you are using) connected to a USB-serial converter connected to your computer.
Option 1: Really easy to build, not-so-low power
An XBee 1mw Chip Antenna can be configured to transmit at whatever datarate you need, has a max. range of 100m, and, best of all, has six on-board ADCs. You can configure the XBee to automatically sample these and transmit their values. X, Y and Z from the accelerometer can go directly into AI0, AI1 and AI2 pins on the XBee and they can both be fed with 3.3V.
- Good: You only need a battery, the accelerometer and the XBee to transmit, and another Xbee to receive.
- Bad: The XBee has 45mA peak current when transmitting.
Option 2: Not so easy to build, low power
The transmitter board you mentioned can be powered by 3.3V (according to the datasheet). Alternatively, you could use this 2.4GHz transciever. In both cases, you will need a microcontroller (easy) or an ADC with serial output (harder, will need a PCB, something along the lines of the MAX1245) to convert the analog signals from the accelerometer to digital signals for the transmitter. I recommend you use a microcontroller (Arduino Pro Mini 3.3V for prototyping, then just an ATMega328 when you're done with the design).
- Good: Low power (7-10mA).
- Bad: Will cost a lot more design time and burnt fingers.
Option 3: Stereo FM transmitters modulating 3 channels of data
This is in response to "Can I do it without converting the signals?".
- Use resistors and op-amps to bring the accelerometer's readings down to 90mVrms.
- Use two of these stereo FM transmitters, hook up X to Rin, Y to Lin, and Z to Rin of the other transmitter.
- Configure the transmitters to Tx on different frequencies.
On the receiver side:
- Aquire the FM signals and demodulate back to right and left audio. You could use something like this.
- Amplify and offset the three channels (right and left channel on one, and only right on the other) to measurable voltages (op-amps would work, but I have a feeling we just added a ton of noise to the whole thing).
- Plug these signals to any microcontroller (Arduino, if you're feeling lazy) with ADCs and send them out as serial data to your computer.
NOTE: Most FM tuners will have band-pass filters that will screw this whole idea up.
I have done many Design Verification Test (DVT) plans and executed them in my past life.
You start by scoping the project with goals, so this answer part 1 to your question part 1.
Plan on many plots of Bit Error Rate BER vs all the above variables
Decide which applications match each setting options
In layman's terms , this is Near Field Communication ( NFC ) radio that is going to change the world in the next 10 yrs. Mobile apps can communicate with any object , a box, a car, your home furnace, your diving buddies and their tank pressure, your SOC medical lab on a chip, etc etc
Why ? because the BOM cost is <3$ in 10k volume
The BA1404 does transmit audio, in stereo.
Whether they are suitable for use together depends on the frequency you use; on whether the receiver circuit will handle the +/-75kHz modulation that the BA1404 will do to the carrier; whether it uses the same time constant for de-emphasis that the transmitter uses for pre-emphasis; whether has a stereo decoder; and of course on whether they are located close enough together for the power of the transmitter to excite the sensitivity of the receiver.
NB The link is incorrect in saying that C13/14 are part of the pre-emphasis circuit. They aren't. It is a simple RC high-pass formed by R6/C15 and R7/C16 respectively. These values will give you 50uS pre-emphasis.
As the receiver is built for 88-108MHz I think it is safe to assume it will handle the modulation, but I don't see any stereo decoder in the receiver circuit. So the answer is 'no' unless you arrange to broadcast in mono, by killing the 19kHz pilot tone in the transmitter, or append a suitable decoder, e.g. the one at http://www.fmmpx.com, which I've built many times for modernising several brands and models of FM tuner.
I would add that the receiver looks pretty basic. I would expect high distortion and poor stereo if any. There are better circuits around. Indeed you don't even need one: just use an old FM tuner. This one talks about component numbers in the text but doesn't show them in the schematic, which isn't too encouraging.