1What are the practical implications of latent mean variance?
All previous multi-group (boys vs girls) test have been non-significant, but this last is significant. Does the variant latent means imply that the instrument is not comparable across gender? Or simply that boys and girls have different latent means?
The means of the latent variables are structural parameters not measurement parameters. If they are different, it means that boys and girls perform differently on that latent variable. For more information on measurement invariance and population heterogeneity, see the Topic 1 course handout under multiple group analysis.