In addition to Jerry's response it's also helpful to keep in mind that 的 wouldn't be required if the adjective were only one character. For example if the sentence were “There is a small bird behind you” then you could simply say 你的后面有一只小鸟. 的 is required here because 可爱 is two characters.

One reason 的 is hard is because there is no functional equivalent in English. In some cases it operates like "of", but in this case it simply indicates a property that belongs to a person or thing. In English you can simply say "a pretty girl" but in Chinese you would say 很漂亮的女孩; it associates the 漂亮 as being a property the 女孩 possesses.

Omitting the first 的 is acceptable.

As Ray says, "你后面" is acceptable. However in my word bank there were 2 "的s"; they may have changed it so it matches with the "official" translation.

Yes. In fact, 在你的后面 would be more commonly used than the Duo version, in my experience.

As far as I know, your sentence is perfectly acceptable.