Can we show the node edit form in a custom block and show that on a node view page?
You could use Form Block module and place the block above your view block. Some details about it (from its project page):
Enables the presentation of user registration, site wide contact, or node creation forms in blocks.
OR go with Clive's answer to this Q: Why doesn't loading a form in the view header work? and load the form in your View's header.