Question

correct sentence for Everybody hopes that the plan would work

Answer 1

The correct sentence is: 'Everybody hopes (that) the plan will work.'

That is redundant here so we can omit it. 'Would' is the past form of 'will' and mainly works as 'modal verb' to express wish, polite invitation, etc. We use Simple Future Tense in combination with Simple Present Tense to refer to a future event or action as in the sentence, 'the plan will work'.