I am building a social page using Community Builder, it is all fine but I am facing one issue that I could not figure out how to do it.
I checked on your demo site and see that, when I open profile of a user, the default tab is the activity tab and I want the same thing for my website

Change the tab order in CB > Tab Management to whatever you like. The activity tab probably has its Display set to Nested Tab Menu. Change that to Tab Menu and make its order as 1 to be the first tab. Nested tabs are shown under the 3 dot menu on the right.

I have one more question, how can I set the adding activity field to be active like when we click to add activity ? This way will make it more visual to users to add activities.

Within CB Activity > Parameters > Activity > Create set "Collapsed" to "Disable".

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That's again just another tab and basic tab configuration. Specifically that's the "User Status", which is configured to display in the "Canvas Main Right" position. Move it to "Canvas Main Middle" and set its display to "Tab Menu" if you want it to be just another tab. I highly recommend reading the CB Primer Book as it covers tab configuration well.