To answer your questions:
1. Does EMSS push to agents or do agents pull from the server?
The EMSS Agents pull from the EMSS Server.
2. Does EMSS use WSUS or Windows Updates on the endpoints?
EMSS Patch & Remediation uses its own content metadata for patch detection and does download its own packaged content for patching.
The patch installations can use the Windows Update engine, assuming it is Windows content being installed.