At present I have two activities setup. One is INTERNET and the other is READING activities.

Both serve different purpose so I require different apps for those.

And I have the habit of keeping the icon pinned to icon-tasks widgets when the app is not running. 
For Eg: In 'INTERNET ACTIVITY' I have pinned chrome and firefox to show icon in Icon-tasks widgets when not running. And wouldn't want to see those app when I am in 'READING' activities. And would like to pin some reading app to the icon-task bar.

But at present when I create a new activity whole of my taskbar is copied to the new activities,
In my case even icon-tasks settings of one acivity is carried over to other activity. So in 'READING' I have chrome and firefox pinned to icon-tasks(even though I dont need them in my present activity'

So I request you to bring in a feature that enables to set even the taskbar widgets and settings only to certain activity.( If other disagree then an option should be provided to disable such sharing of apps between activities).

Reproducible: Always

Steps to Reproduce:
1.Setup 2 activities 'A' and 'B'
2) Open two apps X and Y in activity 'A'
3) Right click on taskbar icon of 'X' and select 'Show launcher when not running' 
4)Close the app.and allow Y running
4) Switch to activity 'B'
Actual Results:  
You will notice the launcher of the app ' X' created in activity 'A' is carried over to activity 'B'. (This is bad)
But the icon of app Y doesn't show in activity 'B' (A good result)

Expected Results:  
The icon of X should not show up in activity B even if it's pinned to taskbar.

Conclusion: 
Recommendation 1) An apps icon whether pinned/unpinned to taskbar, whether running or not running, should reside in it's own activity. (This was the  thing I wanted to tell with above descriptions)

Coming to other finer features:
Recommendation 2) The other way round should be possible ie if I click on firefox from kick-off menu it should take me the activity in which the app resides instead of creating a new window in present activity.
         Suppose, I am reading a book and and have remembered to email a friend a letter, Once I select an app from Kickoff  menu, I should be taken into that activity for further work. When I close firefox I should be transported back to my earlier activity.  

Recommendation 3) There should be a widget/drawer/setting which displays all my 'running' apps from all my activities when I require.