I'm a U.S. native. I've NEVER heard "darl." Never. It actually is difficult and unnatural to pronounce. It doesn't feel right to stop after an "-rl." Even though it's longer, it is actually EASIER to say "darling" (or "darlin'").
"Darling" is common. It is culturally COMPLICATED. Usage is regional or local or personal.
I don't think you should use it. It's not a bad word and it won't insult anyone, but it will sound incongruous and funny to hear a foreign speaker use it.
--I COULD call my wife "darling," but the term of endearment I actually use is "sweetie."
--My first thought was EXACTLY the same as Su.Ki. It is a word that might be used fifty-year-old waitress in a diner talking to customers.
--It is used by parents and grandparents admiring cute children, or a puppy, or a laughing at a baby panda sneezing on YouTube: "Oh, isn't he a darling!"
--If we visit friends and bring a house gift, I can imagine the wife saying something like this: "Oh, you brought me a chrysanthemum, well, aren't you a darling!" Then she would probably gives me a quick "friendly' kiss, a "peck" on the cheek.