The first sentence you have is correct, "John will be washing the dishes at 8:00 tonight." One would not ever say the second sentence. Will be +ed is incorrect.

You can say John will have washed the dishes by 8pm tonight. This is future perfect,-ed is past participle. You can also use a past participle as an adjective. I will be drunk by 11pm!

The first is fine, the second is not proper English. "Will be" is in the future. You can say that "the dishes will be washed at 8 tonight" or "John will be washing the dishes at 8 tonight", not a mix of both. "Ed" at the end of a verb generally makes it past tense. "He washed the dishes (in the past)". "He will be washing the dishes (in the future)".

'To be ___ing' is a continuous tense, 'to be ___ed' is the passive voice.