going to own vs will have owned/been owing

"You're making a huge mistake. My dad is a big-time lawyer. He's going to own this entire building by the time he's through with you."

I'm curious if there should be "will have owned the entire bulding" according to prescriptive grammar?

No

What's the difference in meaning between "He will have owned this entire building by the time he's through with you" and the original sentence?

"He will have owned this entire building by the time he's through with you" is not natural in that sentence.

He "will have owned" often implies he no longer owns [whatever]. Something like "will have taken" means no longer is taking, but has taken and may have already done something else with [whatever]...

I am not an English teacher.

"He will have been owing......." then?

No

He's going to own this entire building by the time he's through with you.
He will own ...
He will have bought ...
He will be renting out ...
He will have sold ...
He will have been able to buy ...

You need to make sure you spell "own/owning" etc correctly. You keep mixing it up with "owe/owing".

What about these two sentences?

"He's going to buy this entire building by the time he's through with you"

OR

"He will have bought this entire building by the time he's through with you"

Use the second.

You can use the first if you change "buy" to "own".