Are league secretaries supposed to submit league averages as of January 1st to the local association so that the association manager can verify them when they are requested for the national tournament?  I have never heard of this in my area.  Our averages are submitted at the end of March or the end of the league season which ever comes first.  Are there suppose to be 2 submissions per league season?

no, but some associations can require it (and they pick the dates). We used to ask for averages just before our association tournament and then final averages.