Which sentence more correct .......?

I would of said, "We will be finished with everything by Friday."

This is not a situation where one is right and the other wrong. Instead, both could be fully correct based on context and usage. With A, there is an implied condition, like, "if everything goes as planned," but, with B, there is no such condition. B simply states when everything should be done (finished). Again, either could be correct.

Correct sentence is :

We would finish everything by Friday

Actually both are grammatically correct I believe but the second one is better for brevity.  You can say " I am convinced we will have finished everything by Friday," just as you can also say, "I am convinced we will finish everything by Friday" it rather depends upon the context of the situation.

It depends what you are trying to communicate. Neither is more correct. Research the difference between the “future tense” and the “future perfect” tense

Both are equally correct grammatically.  The first uses the future perfect tense, while the second uses the future indicative tense, so they convey meanings that are somewhat different.  As such, which one is correct with respect to meaning depends entirely on what you are intending to convey.