How to connect laser with common LD-Anode and PD-Cathode, tied to laser case
Will this laser configuration work with ADN2873?


One thing to watch out for is, your laser spec says you need 2.7 V typical forward voltage on the laser, with no maximum spec. It's not clear to me from the datasheet whether the IBIAS output of the ADN2873 can pull low enough (it will have to pull down to VEE+0.6 V or so) to provide this much forward voltage. The IR laser you mentioned has only 2.2 V maximum Vf, so it might work even if the visible laser doesn't.


  If #1='Yes', what do I need to do differently to hookup the ADN2873? Would I need to use something like an LM7905 to get a negative voltage, and then essentially change all GND's to V- and all V+ to GND in the schematics from the ADN2873 data sheet?


Assuming the laser forward voltage isn't too high, it looks like that would work.

Or you could just put the case of the laser at +3.3 V. You might have more noise in the system then because the +3.3 V node is likely to be slightly noisier than the ground node. And you risk a short circuit fault if some bit of junk falls on the laser (and also contacts some other circuit node). But if you put the laser in a non-conductive case and aren't pushing the limits on transmission distance, both of these issues may be irrelevant.


  If I used the first way (voltage), and the answer to #3 involves using an LM7905, would the voltages from the DAC lines need to be negative too?


Yes, the driver IC will expect the control voltage to be between it's negative and positive supply rails, and will (most likely) measure it relative to the negative rail. Pushing inputs into an IC outside its supply rail voltages will often engage ESD protection circuits on the I/O pins and can lead to unexpected behavior.