"This practice can disrupt the children´s privacy, even though parents are not enough aware of its danger."

"enough" is an adverb that modifies "aware". While there are many exceptions, adverbs usually go after the word they modify, so it should be "aware enough" rather than "enough aware".

Also, "disrupt" is not an idiomatic word to describe what this does to privacy. As mentioned in the comments, more common terms are "compromise" and "violate". We usually use "compromise" when talking about systems (e.g. exploits compromise the security of computer systems), and "violate" when referring to people.

This practice can disrupt the children´s privacy, even though parents are not enough aware of its danger.

This sentence isn't problematic because of the use of enough, but because of the use of even though.

even though - In spite of (something).

Given this, the sentence doesn't make sense. The reason is that we expect a negative outcome if we aren't aware of some danger: disrupting children's privacy is such a negative outcome. Because we expect a negative outcome, we can't use "in spite of" or any of its synonyms. If the parents were aware of the danger, then we could use one of these terms.