Everyone respects her because she is the most competent employee in our company. --**Correct sentence~ ^^ 

I believe your boss is upset, so you had better to go later.

Better say: I believe your boss is upset, so you better go later. 

Can you maintain this condition by this Friday? 

Better say: Can you maintain this condition until Friday?

As the president said, you're going to pay a visit to another country to negotiate.--**Correct sentence~ ^^ 

Believe in yourself. You will do a good job. --**Correct sentence~ ^^ 

I want to pay a visit someone of your company to my office.

Better say: I want to someone from your company to pay a visit in my office. 

What did you do your girlfriend and why she was upset?

Better say: What did you do to your girlfriend that made her upset?

I always want to do a good job every side. 

Better say: I always want to do a good job every now and then. 

I have to negotiate to clients next week. --**Correct sentence~ ^^