Given the narrow range of useful response in both the emitter and detector, plus the interference of ambient IR sources - not really. You might manage in a sealed tube over a distance of a few cm, but it's not practical over any distance. The inverse square law would require a recalibration every time the distance changed to reset the end points of response.
depends what you mean by digital. could convert voltage to frequency and transmit that. Since the frequency is a continuous value some would consider this a analog signal. Pulse width modulation might be considered analog as well. What is wrong with digital anyway? I would think you would want to do it the simplest way that is adaquate, not by prespecifying the technology.
It's possible, but not recommended. You'd need to bias the audio signal so it's always in the "lit up" range of the LED, and even then the LED characteristics are quite non-linear, so you'll have lots of distortion. I'd be tempted by a quasi-digital approach:
Transmitter: Create a pulse-width-modulated (PWM) signal from the audio. This can be done simply with one decent comparator - feed the audio into one input, and a triangle wave into the other input. Remembering Nyquist, make the freq of the triangle wave at least 2X the max audio freq.
Receiver: From a digital output (photodiode goes into transimpedance amp goes into a comparator), just reconstitute the audio with a low-pass filter. An RC filter should suffice if the sampling frequency is high enough.
There are infrared headphones, speakers and conference translation products available. They modulate the IR with ultrasonic FM so the distortion and interference are extremely low.