I am wondering that whether this source is constrained or unconstrained, or mixed.
It depends on the forward model you are using. If the comment of your head model says "mixed", then when estimating the sources you can compute only a "mixed" head model, the options about source orientation are disabled in the "Compute sources" options. Depending on the DBA atlas, some regions will use constrained dipoles locations and orientations and others unconstrained dipole orientations. See the reference articles for more details.
I estimated sources for every run and made a weighted average for each subject. Then I processed baseline normalization (Z-score transformation), Rectify(absolute values) and Project(project on default anatomy: surface).
Projecting mixed models to a template works but is not accurate. The cortex registration between subjects is reliable (based on the registered spheres of FreeSurfer: https://neuroimage.usc.edu/brainstorm/Tutorials/CoregisterSubjects), but the subcortical structures are not. The various volumes are not correctly co-registered - you can see the results of this registration when running the projection, and therefore the interpolation of source maps between subjects is not very precise.
A simpler and less random approach for group analysis is maybe to use volumes source models, and volume scouts to represent your regions of interest.
https://neuroimage.usc.edu/brainstorm/Tutorials/TutVolSource#Volume_scouts
https://neuroimage.usc.edu/brainstorm/Tutorials/CoregisterSubjects#Volume_source_models
If you want to go on with the your pipeline with the mixed head models: if you are getting errors when projecting the source maps, update Brainstorm. I've just found a small bug that is now fixed.