With respect to the letter, in what manner does the warrant change things? Like many have said before, they are still capable of viewing information about the emails that justified the letter (to/from, originating location, destination, attachment file names and sizes, dates, etc).

As far as the Trump Server / Alfa Bank story that's been everywhere, nothing there indicates that trump is involved in anything malicious. I will quote the NYT article (probably to your disliking but I think it includes a key piece of information that is not described anywhere else about the nature of the network traffic between the servers).

Computer logs obtained by The New York Times show that two servers at Alfa Bank sent more than 2,700 “look-up” messages — a first step for one system’s computers to talk to another — to a Trump-connected server beginning in the spring.

If you have a basic knowledge of distributed networking (peer-to-peer) then you know a lookup message is basically one server asking "hey, are you the guy I send this information too"? Infact, there are many common distributed networking attacks that take advantage of lookup messages to overload networks (a type of denial-of-service attack). I'm not saying that this is what the Alfa Bank server did because it clearly did not. I'm just trying to point out that it's not a black and white issue and with no evidence that the Trump server even responded to the lookup requests, it's probably an erroneous lookup request. Even still, a lookup request contains no real information. If nothing else was sent except for a lookup, then no real data was exchanged other than what amounts to a "hey, are you the guy I'm supposed to meet?"

If you want more detailed explanation of a lookup message, you can find information here from the Microsoft Developers Network under DRT (Distributed Routing Table) messaging.