In Canada it is widely considered to be grammatical and in the US it is widely considered (outside of some parts of northern New England) to be incorrect. I'll admit I don't know with certainty what is kosher across the pond, but I've only ever heard Canadians say this so if you're writing an essay to Oxford you'd be safer to go with "done with dinner."
Correct grammar would be (present tense) "are you doing your shopping", or (past tense) "have you done your shopping".
Yes, "The war is done" is grammatically correct but slightly less common than saying "The war is over." Both convey that the war has ended.
Yes, that is correct grammar.
Yes, 'you were correct' is perfect grammar. An example sentence: You were correct when you said that a tomato is a fruit.
This should say, The next stop will be somewhere in Vasayas, then it will be correct grammar. Written as it is it is not on correct grammar.
No, it is not correct
No, "Is was able to confirmed" is not correct grammar. The correct phrase would be "It was able to be confirmed."
Yes
Absolutely.
No, The correct grammar for this sentence would be, "He finished doing his homework."
It is not correct to say "they has studied". The correct way is to say "they have studied." There are many different places that a person can check grammar questions such as English grammar websites.
Yes, it is correct. "Eating dinner" is a common phrase used to describe the action of consuming the evening meal.