Ahmed,
For the 2 groups vs 3 groups solution, you need to look at the goodness of fit measures (particularly BIC and CAIC) and then at the "story" that the between-segments differences in utilities tell in both of your solutions and decide which makes most sense for your study.
Once you've decided on a solution, then you can export the modal segment memberships, which will be categorical variables, and then run chi-squared tests on any categorical profiling variables and ANOVAs (or t-tests) on any metric profiling variables to see how strongly the latent classes relate to the profiling variables.
Be careful about how much adding you do, because even the profile case of MaxDiff doesn't necessarily support an additive composition rule.