can i manage (edit or add) contents of page builder while it is in unpublish condition?

Yes, you'll have to initiate the correct document.

Somewhere in your controller you might have something like:

HttpContext.Kentico().PageBuilder().Initialize(detailModel.DocumentID);

As long as you make sure that document ID is the correct unpublished version or correct workflowstep.

You can detect if you're in edit mode using something like:

bool previewEnabled = System.Web.HttpContext.Current.Kentico().Preview().Enabled;

Making the final result something like the following simplified code:

            if (previewEnabled)
            {
                // get last page version keeping workflow in mind
                ...
                detailModel = something();

                //initiate page builder
                HttpContext.Kentico().PageBuilder().Initialize(detailModel.DocumentID);
            }                
            else
            {
                // get last page published version
                ...
                detailModel = somethingElse();

                //initiate page builder
                HttpContext.Kentico().PageBuilder().Initialize(detailModel.DocumentID);                
            }

I'm actually a little surprised though that the Page Builder is not showing the current checked out version, the Page builder should take care of that, is it not? WHen you edit widgets, aren't they saved to the current unpublished version?

As for the rest of your content, when getting your data, you need to modify your document query based on the environment. The precise code difference in your query would look like this:

if (EnvironmentHelper.PreviewEnabled)
            {
                RepeaterQuery.LatestVersion(true);
                RepeaterQuery.Published(false);
            }
            else
            {
                RepeaterQuery.PublishedVersion(true);
            }

If you want, here's a link to my Document Query Helper for MVC, it mimics the Portal Repeater and handles things, i have an EnvironmentHelper that gets the PreviewEnabled in a separate class (Just returns HttpContext.Current.Kentico().Preview().Enabled; )

https://pastebin.com/eDQrySSk

When using workflow your edit might not be the last published version. The page builder just initiates with whatever Document ID you give it. But that should match your view with the correct Widget Zones :)