Need help in the K2 Worklist webpart.

With the out of the box K2 Worklist there is not an option to disable that functionality at the web part level.  However, in the process on a client event basis you can choose not to make the actions available by taking off the "Make the action available without opening the work item".  Note unchecking this item also disables the SmartActions email approvals as well.

K2 has posted the source code for the web part so if its an absolute hard requirement I imagine you could modify the source to remove it. 

In my experience some of the business owners have asked about removing the actions dropdown in the webpart thinking it would cause problems.  However, in production the end users didn't seem to have a problem with it.

1) Please can you tell where and how can I uncheck the "Make the action available without opening the work item". option ?

                In the actual client event when you go through the wizard on the Configure Actions page.  If you choose the existing action and choose Edit you'll see the checkbox for  "Make the action available without opening the work item".

In the help you can lookup this feature at:  Designing > Designers > K2 Designer for Visual Studio > Design Tools > Toolbox > Understanding Events > Client Events > Configure Actions

2) Another thing I don't want options from the webpart (approve/reject) totally in user task list on the landing page if I uncheck it would that be available afterwards (once the user has opened the task list) ?

                If you uncheck the option "Make the action available without opening the work item" in the K2 Worklist for that task the Action option will still be there but it’ll say something like “you must open the form to complete this task”.

3) How to keep only Open & redirect options only ( open,release,sleep,redirect,delegate,datafields,viewflow,action > approve/reject )   in the dropdown in front of the task ?

                You can’t using the out of the box K2 worklist.