Grammatical problem

The first two are both OK, but I would use should wear as it says the same thing with fewer letters.

The second one is the people. You're only required to be friendly to the people you meet in a professional capacity, outside of work you can be a right miserable bastard.

Many people are, if you're forced to keep a fake smile on your face during working hours you're not going to be grinning on the bus home.

Is it OK to say " you will contact with" ? What if I used " you will have contact with"? Which sentence is more natural? And why?

I would say: The manager will expect that you will cooperate (or work well) with your colleagues (co-workers) and be pleasant to the customers.

And, as Izzy said, "you should wear"

You will contact, drop the have and with.

Or you will be in contact with.

" your partners" (in a security company). Why did you replace the word" partners" with " coworkers or colleagues"? Is it incorrect?
More explanation please!!!

Partners is generally used when two or more people have invested equal amounts into the company. Like attorneys. When you work WITH people, they are your colleagues or co-workers, NOT partners. When you work FOR people, they are your boss and you are their employee or subordinate.

People can be "partners in business" and that is a recognized term. But the people on the floor doing the work are not generally referred to as "partners", although they might "partner" with another worker for a specific task.

co- workers

Customers or clients.

Co worker is an Ametican term, in the UK we say colleague.