Question: Can I use this epistemic expression: “He ***won’t have gone*** there yesterday”? It may not be ungrammatical, I think. But I have two questions. First, is this ‘*won’t have p.p.*’ used casually or freely to say that something might have happened in the past? Second, If it were present perfect, adverbs which denote the past would not be used. Then Is it, *yesterday*, okay in the example above?

Answer: 
I may be the contrarian here but I see a completely possible reading involving the future. Your example may be some dialect which I don't know and I'd be curious to see more of the context, but my interpretation is as follows:

Imagine that your sister is taking her boyfriend out for his birthday and you suggest that she take him to the State Fair, which started a few days ago. She might reply:

> 
> He won't have gone there yesterday?
> 
> 
> 

She's asking whether, in the future situation, he will already have been to the fair. This is proper English.
I've been in the US for 7 years (in the metropolitan area around Washington DC) and haven't heard the FUTURE perfect tense (will have + p.p) used once to indicate something in the PAST.

In this case I would simply ask "Didn't he go there yesterday?"
In an informal context, you may ask "Hasn't he gone there, like yesterday?" This is a short form for "Hasn't he gone there? I thought he went there yesterday."