Please let me know what is right!

"Evaluates" to go with "company", a singular noun.

The sentence is a wee bit clunky. To improve it a little, try

"We hope that the Company will positively evaluate DSA's shipbuilding capability and capacity for the heavy transport vessel, in coordination with reliable project management and operation by MEGA for the project's success."

or, "...for the success of the project."

I am somewhat surprised by McT's "response. I may be wrong about this, but it has been my experience that in British English, a singular noun such as company is often treated as a plural noun. So, it might read "the company evaluate," rahter than "the company evaluates." I'll accept, of course, what he says. In the American usage, it would always be treated as a singular noun--"the company evaluates.

It can be.
"The Police" and "The Army" can be seen as singular or plural.

examples
The police believe crime is declining. (pl)
The police is a good career for a youngster. (s)
An army marches on its stomach. An army of ants invaded the picnic. (s)
The army are in open revolt. (pl)

All quite correct and grammatically acceptable, I think.