"I am sad and they are happy."
Translation:אני עצוב והן שמחות.
The third is incorrect because of the second clause. הן is they (fem.) plural but שמחה is singular (fem.).
Yes both genders are correct, but since you used the word "הם" In your sentence, which is masculine, then you have to use the masculine form of "שמחות" too which is "שמחים".
So the complete correct sentence would be:"אני עצוב והם שמחים"