Issues after replacing a new rack and pinion?

The Air Bag light is likely due to a broken clock spring. That's a wound-up ribbon cable in a plastic housing under the steering wheel. That can only wind up and unwind just slightly more than the steering wheel can normally be rotated lock to lock. If the steering wheel is rotated one or more revolutions either way while the steering shaft is disconnected from the rack and pinion assembly, the clock spring will no longer be centered. It will either wind up too tightly and tear apart the first time the steering wheel is turned to one side, or it will unwind and fold over on itself when rotated fully the other way. That one takes a number of events before the cable will crack. Either way, once that ribbon cable breaks, it will be detected by the Air Bag Computer. It will set the fault code, "Open Squib", or "Open Initiator", turn the system off, and turn the warning light on to tell you. We'll need to discuss replacing that clock spring once the steering issues are sorted out.

When you count the turns for the outer tie rod ends, that is only going to get you in the ball park. As little as a half a turn on one of them is enough to take you from acceptable tire wear to a miserable wear pattern and poor handling. There's absolutely no way you're going to get away without having the car aligned, so what you're after is to adjust each front wheel close enough to allow you to drive the car to the alignment shop.

Start with the steering wheel centered, then rotate it fully each way and see if the steering wheel turns roughly the same number of turns. I think you're going to find that is okay. To be off a difference of even half a revolution would mean the tie rods are adjusted so unevenly as one of them would come apart. It's still a good indication you did the steering gear job correctly.

Once you verify the steering wheel is centered, lock it there, then adjust each outer tie rod end until each wheel is close to parallel with its rear wheel. That will let you drive it to the alignment shop.

Let me know how you make out with the alignment, then we'll tackle the clock spring.

No, don't cut anything. Even if for no other reason than liability. Are you able to compare the length of the new inners to the old ones? If they're different, it's safe to say you were handed the wrong parts.

Don't get excited if the new tie rod ends don't screw together the same number of turns as the originals. That's a valid observation to show you have the right parts, but no two parts are ever exactly the same. To have two tie rods four to six turns different than the originals is not uncommon.

In case I missed something, do I understand you screwed the tie rods together as tight as possible? If so, that is the problem. The last step of the alignment procedure is to lock the steering wheel perfectly straight, then adjust each pair of tie rods to bring that wheel straight. The locknut holds them there. The best you can do is get each wheel adjusted as close as possible to straight ahead. Those adjustments will be fine tuned during the alignment.

Let me know if I'm on the right track.

Dandy. Ask if they will give you a printout of the alignment. All alignment computers can do that but most mechanics don't bother unless asked. If you do get one, post it for me to interpret. Will wait to hear some good news from you.