I know this question was posted a few years ago, but I ran into the second problem listed here and thought I would post how I solved it in case anyone else runs into it.
When results are sent to the parameter and covariance data sets, the parameter names in the parameter data set have a set length of 20 characters. Thus, in the parameter data set your parameter name is being cut off at days_cough_duration_. In the covariance data set and your MODELEFFECTS statement in PROC MIANALYZE, however, it is still days_cough_duration_numeric, and so the names don't match and SAS thinks it doesn't have the estimates for the variable. Change the variable name to a shorter one and it solves the problem.
For the first question, it seems that having between-imputation variance of zero would indicate that there were no differences between the results for the imputed data sets, and thus no differences between the imputed data sets for these variables. If both variables are dichotomous and you had a good number of predictor variables and few missing, this seems reasonable. I tried this with my own data, with two dichotomous variables with only 1 missing respondent per variable. The imputed values were the same in each imputation, and when I ran PROC LOGISTIC and then PROC MIANALYZE I got the same warnings you did.
I had the same problem. When I looked more, the output table of estimates truncated long variable names. Then, with selecting shorter variable names, my problem was solved. I'm not sure if you have the same problem.
Just rename and create a shorter variable name, and it could be fixed.
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