Do we have to create a dry well for draining of the regenerated water?

I would expect that it would possibly kill your plants. The air-gap requirement is to keep waste water from accidentally entering the system should something go wrong. I have it connected to my washing machine drain, and have a septic system. There is conflicting information on this, but seems to work fine for me and others in my neighborhood. Search online and you'll find adapters to give you the necessary air gap and allow you to easily hook it to the washing machine drain.

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A drain is needed for regeneration water. A floor drain, close to the water softener, is preferred. A laundry tub, standpipe, ect. are other drain options. If these options are not available, we recommend that you look into your local plumbing codes for further options. If you have any further questions please feel free to contact our customer support center at 1-866-986-3223. Thank you!

The air gap is to keep potable water (what we drink) separated from waste water. That's what the air gap does--any overflow or sewer backup can't reach the potable water. How you run that is up to you, your plumber and local code (plumbing codes vary widely). In my instance, we built a typical shower trap (the loop that contains water in it to prevent sewer gases from coming into the living space) and suspended the line above the top of the trap. That gave us our air gap but contained the water. The output from the recharge cycle of the softener is pretty heavy--something like 20 gallons at full pressure--so plan for that. Try to avoid running the waste into any septic systems, but local sewer should be fine. Again, check with your local building inspector for plumbing specifics. If you want to run it outdoors, make sure it's away from the foundation to avoid water pressure on foundations or seepage into basements or crawl spaces. As for how salty it is and how if affects plants, I can't say. A dry well that is downslope from the foundation and a good distance away would be a good choice.