Yes, the phrase "last evening" is correct and commonly used to refer to the evening before the current day.
No.You rather say,[Having dinner or simply dining].
If you are referring to this sentence, no, it does not resemble a correct phrase AT ALL.
Did they....?
No, "ad verbatim" is not a correct phrase in Latin. The correct phrase would be "ad verbum," which means exactly, word for word.
The phrase "how don't I" is not grammatically correct. A more correct way to phrase it would be "why don't I."
last night, yesterday evening
It's correct.
The correct phrase is "an evening." The article "an" is used before words that begin with a vowel sound, and "evening" starts with an "e" sound, which is a vowel. Therefore, you would say, "an evening" rather than "a evening."
Yes, as in "For the evening meal, we plan to commence with a soup course.". "commence" means "start".
"In the evening"
Both are correct; however, the more concise and therefore more elegant usage is "by evening."
a wonderful
No.You rather say,[Having dinner or simply dining].
'The evening news' is Finnish is 'iltauutiset'.
It is somewhat archaic. You could say "Mr. Jones goes out for walks of an evening" which is correct, but which also is not how this idea would usually be conveyed. In modern usage it would be more normal to say, "Mr. Jones goes out for walks in the evening." There are other possible contexts for that phrase as well such as, "Evening is my favorite time of day; I never get tired of an evening."
'In the hope that' is the correct phrase.
If you are referring to this sentence, no, it does not resemble a correct phrase AT ALL.