PHY Register 5 Technology Ability Field Meaning
Yes A2 corresponds to half duplex; this is implied by A3 being explicitly specified to be full duplex.

I have a copy of the 2008 version of 802.3. Annex 28.B.3 specifies a prioritization scheme as follows (from highest to lowest):


10GBASE-T full duplex
1000BASE-T full duplex
1000BASE-T
100BASE-T2 full duplex
100BASE-TX full duplex
100BASE-T2
100BASE-T4
100BASE-TX
10BASE-T full duplex
10BASE-T


The spec provides the (performance based) rationale for this, stating: Full duplex solutions are always higher in priority than their half duplex counterparts.