Not very, engineers are good at doing things, not explaining things, if they were good at writing papers, they would be managers, but at that time, they would write more and do less in the field. Math is the more important subject at hand, not writing.
No. If you're bad at essay writing, you might as well just get used to saying "You want fries with that?".
Classes in writing are are typically required to earn a degree in science and engineering. Those classes determine whether or not a student has sufficient writing skills for science and engineering careers.
Math is good for science and engineering of any type.
That is possible, but it depends upon how bad you are at essay writing. You should probably ask your tutor to evaluate your essay writing and give an opinion of it. Hopefully you have a good tutor who is capable of doing that.
In most cases, no, but it will depend on the instructor. It shouldn't though.
Pretty much, don't go for the following: English Literature History Psychology Sociology Anthropology Philosophy Humanities any Social Science major(except geography)
It sure helps if you're good at arriving at precise calculations. However, being "bad at essay writing" is not a benefit; it may be less of a detriment in engineering than in, say, English, but it's possible to be an engineer and a good writer.
Any field will eventually pose a challenge for someone who is weak in essay writing. The best solution for the problem is to improve your writing skills, and the best way to improve your writing skills is to A) take more writing courses than simply those required for graduation, and B) write as much as possible - essays, articles, papers, etc. Never simply resign yourself to being bad at essay writing. If you think or know that you are, do what is necessary to remedy it.
students
Clear writing is a valuable ability regardless of what vocation you choose, but the lack of this ability will be more of a handicap in the liberal arts (English, literature, history, etc.), so in choosing the lessor of two evils engineering would be a better choice than liberal arts. Science requires writing many scientific papers, so demands writing skills more that engineering does.
Yes
Writing an essay about why science is important will teaching you why it is important. You will learn how to actually use science in your life.