Just as the definition by dictionary, the explanation by Alexander would be correct. However, as the Japanese custom, おんなのこ can also refer to young girls whose ages are around twenty and sometimes around thirty without including children. We say e.g. "会社<かいしゃ>の女の子 girls in the company" in casual conversation. As the Japanese custom, おんな implies glamorous and sexy women. You should use 女性<じょせい> for women. As for the nuance of "あいしています" I agree with Alexander. BTW, あいしてます works. You can informally omit い as in います. Personally, I think "だいすき" in this case still implies like you are addicted to Japanese girls. Simply, "すきです; like" would be fine. You can say: (わたしは)　日本（人）　の　じょせい　が　すきです This means you like Japanese women regardless of the ages, implying that you may like their personality, behavior, custom etc. （わたしは）　日本（人）　の　おんなのこが　がすきです This may imply that you want to get a young Japanese girlfriend in addition to that you like their personality, fashion etc. Be careful to use this sentence.

Um, technically yes, though this may be an especially creepy way of doing it. There are 2 main problems I see. おんな literally means woman/female, and こ after おんなの means child, so that means you generally like younger girls, bending towards children. >.> The other is あいしています (a little spelling correction as well), as this is typically viewed as the strongest form of love, so much so that sometimes not even married couples say it. I've heard it used between family members as well as couples, but this is way too profound/strong for the context you're trying to express. Simply 「わたしは　日本人の　おんなが　だいすき　です」 would be fine.

私は日本人の女の子愛してます。