Does the ES2 managed Ethernet Switch module 4 x 10 Gbps fiber optic ports option support full auto-negotiation and auto-MDIX?

No, the terms “auto-negotiation” and “auto-MDIX“ typically apply to the 10/100/1000Base-T (copper ports). However, each of the (4) FO ports can be configured independently by the customer in the field; it’s just a setting like any other port setting in the management console and each port can be toggled from 10 Gbps (default, from factory) to 1 Gbps (and vice-versa).