- All lessons are cancelled today because of weather bad condition.
- I'm freezing of the cold.
Are they grammatically correct?
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The word bad is an adjective and it should describe the noun phrase weather conditions (weather bad condition makes no sense whatsoever). Notice the s on the end of conditions that marks it as plural. Otherwise, to be grammatically correct, you would have to place an indefinite or definite article in front of the whole thing. But in this case it necessarily should be plural because weather conditions is a standard phrasing commonly used in this sort of situation. So, I recommend rewriting your example like this:
All lessons are cancelled today due to bad weather conditions.
If the effect that you're trying to achieve is to sound a little bit more formal as is typically the case when it comes to public announcements and such, then in that case the expression due to sounds like a better choice than because of. The expressions themselves basically mean the same thing. The only difference is in the level of formality with which you use them.
Although the second sentence is comprehensible to a certain extent, it's not, strictly speaking, very coherent English. If what you're trying to say is that the reason you're freezing is because it's cold in the room you're currently in, then the following sentence would be a better way to phrase it:
I'm freezing because it's cold in here.
If, on the other hand, what you're trying to say is that the reason you're freezing is because the weather today is cold, then we would have to make some minor adjustments to the previous example like this:
I'm freezing because it's cold today.
I'm freezing because it's cold outside.