I need a deep explanation with examples.

That's a bit of a tough order but I shall try to deliver.

Overall would is the past tense of will. Will is the future tense. Is is the present tense and it's a little difficult to explain be these are verbs on the state of existing.

He would like that.
He will like that.
He is liking that.

They're all interesting also becuase they imply a certain amount of confidence in their usage. See for example would vs may. May allows us an open-endedness we don't generally have with would; ie the ability to be unsure about our assurance. Sometimes would can be "unsure" (example: "Would it really affect us that much?"), but that's a different kind of uncertainty. You could replace would with could and it introduces a different kind of uncertainty to the question. Could it do this? We're not sure. Would it do this? Maybe, since it doesn't seem too far out of character.

Would be...

Right off the bat I can only think of the use in a question and not exactly the usage of "be" since "be" is a different tense. You'd have to use being becuase the usage of being requires you/it to already have been. It could have just become (or became), or whatever related applicable word you want to use. It doesn't matter, what matters is that it has been in some form.

"I really don't know why I reacted like that-"
"Would being an idiot have anything to do with it?"

First off this is sarcasm, which has it's own logic and really messes with you. A legit "would question" is above.

Would starts the question asking about whether so-and-so is an idiot and if some apparently terrible outcome is the result of them being idiotic. They're talking about an event in the past so to reference that event they can only use past tense verb. The responder thinks so-and-so is an idiot, and this is in use an insult. The rhetorical answer to the rhetorical question of would being an idiot make someone do that is yes, yes it is. Before we compare, take a look at would have to be.

Would have to be...

This usage still requires something to have been. The difference is it applies it differently. Would be is more cause-oriented, would have to be is more result-oriented. Take a look below.

"You would have to be an absolute idiot to fall for that!"

Would being cause it vs You'd have to be to do it.

Will be...

Will be is essentially the same as will become. Usually will become is clearer than will be becuase be is a weird mesh of tenses (example: "It must be." vs "Be all you can be.").

"What will she be when you are done with her?"

Be is the verb of existence, different than is which is the verb of existing.

Will have to be...

Again the difference between Will have to be and Will be is that Will be is cause-oriented while Will have to be is result-oriented.

"They will need to be, otherwise the last of the light will go out."

Yes I replaced have with need, since they're very similar in use. However, need vs have is a different question.

Will being do this vs Something will have to be to do it.