You could probably just set the voltage to 5+ volts and as long as you don't increase the current past it's max input then it will only use the voltage it requires at the given current. I'm not saying to do that but I do it all the time and it's fine. Laser diodes need current regulation more...
As the current increases so will the voltage requirements. If you have it locked at 2.2V then you won't be able to go any higher with the current. Try setting the voltage to 2.5V and slowly increasing the current from 0V. You may need to go even higher than 2.5V to get the full output but that's...
It depends on the diode but most of the higher power multi-mode diodes have pretty terrible divergence. A beam expander will help quite a bit though depending on exactly how far you're trying to point.
It mostly has to do with new shipping regulations. Lithium batteries aren't allowed to be sold separately in marketplaces like Amazon and Ebay anymore unless they come pre-installed in the equipment.