1) How large is the first party base segment? If it’s on the smaller side, it could be causing issues. In addition, I would look at the overlap between this segment and the Acxiom 3rd party traits via an Overlap report to determine how good the overlap is for modeling purposes. If possible, you may want to consider trying a different 3rd party data provider for comparison.
2)Please see above. How large is the algorithmic trait that you can generate from the model? If it’s not very large, I’d look at some of my suggestions in (1).