No, this is not correct. The word "vow" is a singular noun, and you can speak of making "a vow" (it's like a pledge or a promise). There is a word "avowed" but it's an adjective, and it means someone who declares a certain belief openly. So, you make "a vow" (it's two words) to be an honest person. And someone can say they are an "avowed" (one word) atheist.
An avowal is a declaration of affirmation or an admission of knowledge.
'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.
This is not a sentence it is a phrase and as a phrase it is correct.
avow
The correct phrase is "Did they?".
That is the correct spelling of "phrase" (word group, or to use specific words).
The correct phrase is "sufficient proof".
It depends on how you use the phrase: Can you provide me a copy of your CV? - correct
No, the correct phrase is veni vidi vici.
To correct a dangling infinitive phrase, you should make sure the phrase is properly connected to the noun or pronoun it is meant to modify. You can rephrase the sentence to include the subject that the infinitive phrase is describing, or you can place the subject immediately after the infinitive phrase. This ensures clarity and avoids confusion about what the phrase is modifying.
No, the phrase "it is well" is not grammatically correct. It seems to be missing a verb or adjective to complete the sentence. You could say "It is well done" to make it grammatically correct.