Who has the server?

The good guys

Why does POTUS continually refer to the server?

POTUS does not speculate.

Because he wants to force fake news to report about it because of upcoming massive exposure

Who has it all?

The good guys and I believe JA will play a big role into this. Ecuador is just about to hand him over to UK and in return UK will extract him to US(this won't be filmed though since JA hasn't been at the embassy since december, unless he wants to take the risk and go back to the embassy) VP Pence's visit to Ecuador late june certainly made Ecuador to do this. Not only will the server information lead to massive arrests, It's very likely JA will inform us that Wikileaks is fully controlled by CIA and destroy Wikileaks in its current form. JA's extraction is supposed to take place this week so july is indeed the month people learned the truth.