It is a colloquial phrasing, because you are using "really" to mean "extremely" and "badly" to mean "desperately" or "greatly." A less colloquial form is very badly.
No, "really badly" is not grammatically correct. It should be "very badly" or "really bad."
Yes, "she sings badly" is grammatically correct. The adverb "badly" is describing the verb "sings" in this sentence, indicating the quality of her singing.
The phrase "You are not knowing" is not grammatically correct. Instead, you can use "You do not know" or "You are not aware."
Yes, "He sailed his boat on the river" is grammatically correct.
The phrase "Is you don't miss me do you" is not grammatically correct. It should be rephrased to something like "Don't you miss me?" to be correct.
No, it is not grammatically correct. The correct way to say it is "your older sister."
Yes, "she sings badly" is grammatically correct. The adverb "badly" is describing the verb "sings" in this sentence, indicating the quality of her singing.
It certainly can be correct. As with all grammar it depends on how it is used
Technically both are grammatically correct, but it really depends on how you are using them and what context they appear in.
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"Not like that" can be grammatically correct, depending on the context.
Yes! That is grammatically correct!
Yes, 'for free', is grammatically correct.
Neither really. 'In' would be the word to use.
The phrase "You are not knowing" is not grammatically correct. Instead, you can use "You do not know" or "You are not aware."
"That was wrong" is a grammatically correct sentence.
Yes, it is grammatically correct.
Yes, Almighty God is grammatically correct.