Is there a way to display some content fields in a separate block? I would like to display some content fields in a separate block so that I can manage the position of these like other blocks and also put them near to other blocks such as the search widget.

I am using display suite for laying out the content but don't think that this will serve my requirement to position some content fields further away from the the main content. One specific example I have is displaying the content's taxonomy fields below the search widget (which is in a block).
You could create a view which selects the field you want from a node. Use contextual filters to get the Node Id in your view.