It seems that she wants to say a few words to her team leader. -- *Correct sentence~ ^^ 

He is your family, but he is in the opposite team right now. --*Correct sentence~ ^^ 

Some people always speak negative.

--> Some people always speak negatively. 

Do you want to ask me that I cheated your friend? Not at all!

--> Do you want to ask me if I cheated on your friend? Not at all!

She is hardworking more than anyone else. --*Correct sentence~ ^^ 

Everyone likes him because he always works proactive even though it's not his job. --*Correct sentence~ ^^ 

It's so cute that her son wants compliment anytime.

--> It's so cute that her son wants a compliment anytime.  

My mom always praises me whatever I do.

--> My mom always praises me in whatever I do. 

Let's come up with a fabulous idea for next week's meeting. --*Correct sentence~ ^^ 

We hereby strongly suggest to discount 5% of all.

--> We strongly recommend a 5% discount on all.