Hi Steve,
1) The number of iterations will vary from imputation to imputation within runs of amelia(). This is important because it means that you will get different imputed values across the "m" imputations. The seed should make the entire run of amelia() the same as the next run of amelia(). Thus, "Imputation 2" in one run should have the same imputed values as "Imputation 2" in the next run with the same seed.
2) This is probably due to highly collinear variables in the dataset or a linear dependence in the data. You might check for a saturated set of dummy variables or linear transformations in the data and set those to "idvars".
Hope that helps!
Cheers,
matt.
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Matthew Blackwell
Assistant Professor of Political Science
University of Rochester