Learn English – is “unlucky you” idiomatic like “lucky you”

When saying goodbye, take it easy and take care are virtual equivalents. I wouldn't construe either one to mean anything more than a polite yet standard way of saying goodbye when two people depart from each other.

I also would like to know what situations I can use the phrase "Take it easy."

There are several uses of that phrase besides the standard goodbye. In context, it can be used when:

• you try to calm someone down (Bob was about to get in a fight when his friends told him, "Calm down, take it easy.")
• you want someone to be cautious (Jill was teaching her daughter how to drive, when they approached a sharp turn in the road. "This road takes a sharp turn up here," Jill said. "Take it easy on this curve.")
• you want to tell someone they should embrace a more carefree lifestyle (Ted said to his friend Janet, "You stress out too much; you should just learn to take it easy.")
• you want to help soothe or calm someone's anxieties or emotions (Brenda broke down in tears when she told her husband the bad news: she had just lost her job. Her husband embraced her, and tried to offer some reassurance. "Take it easy, honey," he said. "Maybe this will work out for the best somehow.")

Similarly, "take care" is usually just a shortened form of "take care of yourself," which is why some folks may say that to you when you're not feeling well, either physically or emotionally.

Both phrases often have undertones of empathy, although "take it easy," usually means to slow down or relax, while "take care" means to get well, or remain in good health or spirits. As I said before, though, when either of these are used as a substitute for goodbye, there's a good chance the speaker used one instead of the other only arbitrarily, unless something earlier conversation might have changed that.

Your first instinct is correct; this is a noun adjective construction. It does indeed look like the keep something in some condition construction, but that doesn't make sense semantically. It's keep in the sense of retain possession, which is often used to indicate that something else is more desirable or better, as is the case here. The Hogwarts Sorting Hat is the best hat there is, so "you" can keep all the other hats, as they are unnecessary.

Why is the usual word order reversed? Because this is a poem and the author wants to maintain a meter. Black bowlers would make two stressed syllables sequentially spoken, and break the rhythm.