Summary:

No, the filing does not allege payments from the Clinton campaign (or its lawyers) to Neustar (Internet Company-1), and nobody has claimed such a thing until now. The only payments alleged by John Durham are from the Clinton campaign to its lawyers, not any payments from its lawyers.

No, there are no servers belonging to the Trump Tower or the White House involved. Actually, there’s no servers involved. The thing in question are Neustar’s DNS logs, which presumably are stored on servers somewhere, but this isn’t really relevant (you wouldn’t accuse Neustar of infiltrating it’s own servers).

No “infiltration” happened. The issue is misuse of data legitimately in their possession.

Yes, they misused the data legitimately in their possession for possibly illegitimate purposes — specifically to support conspiracy-theories against candidate Trump.