Q: Do you know if any digitizing approach is available for group projects? In my class groups of students are assigned to build a repository of primary sources and then exhibit their collection.

A: The web publishing platform, Omeka, would work for creating narratives around digital collections. Read about the teaching with Omeka experiences here and here.

Q: The mobile learning seems to be attractive to students in my class. It is easier for them to stay connected while working on a group assignment online. What mobile app would you recommend which is safe to use in a classroom environment?

A: I would recommend ooVoo app - it is free and user-friendly video chat. It can handle up to 12 people at a time. The alternatives are listed here.

Q: developing online course is a project. Do you know any free project management tools available online?

A: this article gives you a list to choose from: http://www.smashingapps.com/2010/02/15/10-free-tools-for-effective-project-management.html
The additional links are in the comments below:
http://www.oneplacehome.com/
https://launch.unifiedinbox.com/
http://openatrium.com/
http://www.gtdagenda.com/
http://www.teamworkpm.net/

etc.

Q: I'd like to create Wiki page for my class. How do I start?

A: Wiki  proved to be a great tool for collaboration. You can request Wiki through ASU Blackboard: http://help.asu.edu/sims/selfhelp/SelfhelpKbView.seam?parature_id=8373-8193-4586 

or build your own outside of Blackboard.

Here is the link to a brief response and resources: https://educators.pbworks.com/w/page/18697857/StudentWikiAssessment
The advantage of using Wiki instead of Google documents is: you can track individual contribution of the student to evaluate his/her participation in the collaborative project: http://community.wikia.com/wiki/User_blog:Meighan/Tracking_Contributions:_Recent_Activity