Thanks for your response Blake,
To be more specific, here is how I set up my environment.
In the screen shot, I have two websites, SimpleWeb and TelliengetCommunity7. SimpleWeb is running TC7 as a virtual application while TelligentCommunity7 is running it without a virtual application.
For SimpleWeb, I created a skeleton web site that has only one page and i have the host entries in my host file (127.0.0.1 simpleweb.com, 127.0.01 www.simpleweb.com). Also, I installed TC7 using this link http://telligent.com/support/telligent_evolution_platform/community/w/community7/24664.install-telligent-community.aspx
Also, I was not able to update my profile and it says "An error occurred while saving. Please review your changes and try again".
However, I was able to create a new user and new group so I think those problems are happening on the specific area.
For the problem 2: Yes, we are planning to call REST API from the external application so I need to create the API KEY that has Admin permission.
If you look at the screen shot below, I was able to create a API Key, admin4 if it was not in a virtual application; however, if it is in a virtual application, I could not create a new API KEY. In that case, nothing happens if I click "Generate" button.
To summerize it, I have no problem with TC7 if it is the own web site (TelligentCommuinty7 in my setup). But, within a virtual application, some functionalities are not working.
Actually, we should finish this probject ASAP, but we are stuck with those problem.
Please let me know if you need any information from me to investigate the problem.