No. If you suck at essays you suck. Full stop!
An engineer or computer scientist may have to write good proposals to get funding. They will need to sell their skills and ideas to prospective customers. Communication with co-workers will require clear instructions. Although some of these things may be done verbally, many will require good writing skills.
Surely no. Whatever may be the field we need good communicating skills. Incase of written exams that will be shown by the essays and description that we are going to provide.
-- No. You should not be ashamed of yourself. -- No. If you fail science and engineering, that won't be the reason.
You need to write this. Wiki doesn't write essays for students.
Not really. Science Engineering deals basically with Math subjects. Therefore, if you're good in Math, you'll do good in Science Engineering.
Other than the science and engineering disciplines(except for software engineering, computer science and biology), most disciplines in the humanities, social science and to a certain extent, businesses that don't require mathematics, paper writing skills are needed in the workplace, even with years of experience won't do you good unless you possess a certain skills set.
Engineering is for students who have a fascination and curiosity for the subjects and tasks that engineering deals with. Others need not apply. It makes very little difference what they're good at or not good at. (Answer written by a person with a piece of paper that says he became an engineer almost 40 years ago, and who is still at it.)
No matter what you study in university, you have to write essays and reports, however, the university majors that have less writing usually fall under the mathematics and science spectrum: Math Economics Engineering
Not necessarily. You're in school to get better at those things.