how to show post of current week

https://codex.www.ads-software.com/Class_Reference/WP_Query
https://codex.www.ads-software.com/Class_Reference/WP_Query#Time_Parameters

example:

$this_week_query = new WP_Query(array('posts_per_page' => -1, 'w' => date('W')));

$next_week_query = new WP_Query( array('posts_per_page' => -1, 'w' => (date('W')+1)) );

(not tested)

if it is the only query on the page, you could also try to work with query_posts() using the same parameters;
https://codex.www.ads-software.com/Function_Reference/query_posts

Should the post be published as scheduled for upcoming weeks, or is there any other ways of adding a “time stamp” if you publish immediately?

If you schedule a post for an upcoming date, it won’t be visible on the site until that date is reached. So if your intention is to have a list of articles about upcoming events that people can read ahead of time, you’ll need to publish them immediately.

If you need to add an additional timestamp, I’d just put it in a custom field and add that field to your template. Or alternatively just use Taxonomy and categorize the posts by day of the week.

Excellent! Got it working. By adding post_status set to publish and future I am also able to list scheduled posts:

$my_query = new WP_Query(array(‘post_status’ => ‘publish,future’, ‘posts_per_page’ => -1, ‘w’ => date(‘W’),’order’=>ASC));