1. People in the Netherlands are surely hoping for another cold winter.

2. People in the Netherlands are surely hoping another cold winter.

3. Surely/Certainly people in the Netherlands are hoping for another cold winter.

4. It is certain (that) people in the Netherlands are hoping for another cold winter.

5. It is sure (that) people in the Netherlands are hoping for another cold winter.
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Are they all grammatical? Are they all the same? Do we have to use 'hope for' or 'hope'? Can we omit 'that' in #4 and #5? Thank you for your help.

#2 is incorrect; the others are fine.

We need "hope for," yes.

It's better to leave "that" in the sentence (4 and 5), but if you omit it, the sentence will still be understood.