How to make a form with latest nodes listing with checkboxes same as in 'admin/content' page?
First off all you can see how this realize in /admin/content page.
The file /modules/node/node.admin.inc has a function node_admin_nodes() 
This function returns form which contain list of nodes. The file has clear description and you can read and copy-paste code from this function to your module with necessary modifications.