Your description of the confusion matrix is correct **assuming alive people are defined as a positive** outcome.  Those entries are the correct order.

    TP | FN
    FP | TN

I do not like how Weka labels the columns.  TP Rate (for example) is based on that row being the positive.  So the second entry under TP Rate (0.626) is actually the TN Rate.  The other columns are defined similarly.  For example: The second entry under FP Rate (0.015) is actually the FN rate.  The second entry under Precision (0.753) is the "Precision" of the negatives (aka negative predictive value).  In other words, the column labels are only correct for the first row assuming the first row is defined to be the positive outcome.

The last row "Weigthed Avg." is not necessary for binary classification.  It is weighting the results based on the sample sizes for each class.  For example the last row first column, TP Rate (0.959), is actually the overall accuracy of the model.  I would ignore this last row.