How does one say "carefree" in German?

Question

According to dict.cc, there are three similar ways to say it: sorglos, sorgenlos and sorgenfrei. This doesn't include the other translations such as unbekümmert or unbeschwert, either! Then which one would I use, and what are the difference(s) between them?

Also, another question that someone could possibly answer: if I am met with multiple translations for one word like this, which one should I use? Sometimes I just choose one randomly, and a German speaker tells me that the sentence I am making sounds really strange, unlike one a native speaker would make.

As a commenter mentioned, here is the sentence I would like to translate:

The children smiled and looked happy and carefree.

Answer 1

It depends in what context the word is mentioned.
An example:

She has a carefree attitude toward life.
Sie hat eine unbeschwerte/unbekümmerte/sorglose/sorgenfreie Einstellung zum Leben.

The translations can all be used here but have a slightly different meaning.

Your example:

The children smiled and looked happy and carefree.
Die Kinder lachten und wirkten sorglos und glücklich.

If it is used as a single word in e.g. insurance advertisements it could also be translated as "rundum sorglos Paket" but this would be a special occurrence.

According to ngrams "unbekümmert" still seems to be the most used adjective of the four given but in most cases all of them can be used with a slightly different meaning. If it sounds strange it does not mean it is wrong.

"unbekümmert/unbeschwert"

is used when you want to express that you do not feel grief about something.

"sorglos/sorgenfrei"

is more likely used when you want to express that you are not afraid of something.