Both are correct but their meanings are not exactly the same. Thought of the day sounds as if it is used after the day. Thought for the day makes more sense before the day or at its beginning.
That is the correct spelling of "well thought out" but a synonymous phrase could be "thoroughly considered," also "contemplated" or planned.
'In the hope that' is the correct phrase.
This is not a sentence it is a phrase and as a phrase it is correct.
It does not sound natural, and the more widely used phrase is "within the day".
In the sentence "He has always thought about his future," the verb phrase is "has always thought." While "thought" is the verb, a verb phrase includes words that may affect the tense of the verb.
That is the correct spelling of "well thought out" but a synonymous phrase could be "thoroughly considered," also "contemplated" or planned.
'In the hope that' is the correct phrase.
This is not a sentence it is a phrase and as a phrase it is correct.
It does not sound natural, and the more widely used phrase is "within the day".
In the sentence, "he has always thought about his future" the verb phrase is "has always thought".
That is the correct spelling of "phrase" (word group, or to use specific words).
In the sentence "He has always thought about his future," the verb phrase is "has always thought." While "thought" is the verb, a verb phrase includes words that may affect the tense of the verb.
The correct phrase is "sufficient proof".
If you are referring to this sentence, no, it does not resemble a correct phrase AT ALL.
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.
The phrase "A dollar late and a day short" is an example of a malapropism, where a word is humorously misused. In this case, the correct phrase is "A day late and a dollar short."