Featured images not showing in archives

I'm working on a page design: http://clone2-musicofnature.mystagingwebsite.com/category/lang-chats/

It's looking pretty good, but:

1) As you can see, it's not displaying the featured images for the posts; is there a setting somewhere for this?
2) I want to eliminate the category lists for each post, which cover the titles.
3) I would like CSS for rounding the corners of the post boxes

Thanks in advance.

 

Thank you very much! The images are now in place, but there are still problems with the image display (white spaces above and to the right):

http://clone2-musicofnature.mystagingwebsite.com/category/insects/

ALSO ... I definitely want to get rid of the categories displaying over the photos. This is because most of my posts are assigned to multiple categories, which creates a mess when they are shown over the images. So there must be some CSS that will hide them. Right?

 

Wow ... it's starting to look great.

Now I just need to reduce some text padding using CSS. See attached for a view of what spaces I want to control: https://clone2-musicofnature.mystagingwebsite.com/wp-content/uploads/2019/07/spaces-to-reduce.png

 

Hmmm ... my attachment (a 250KB png) from my previous reply is perhaps not showing? If that's the case, how can I send you a couple of pngs, one showing the spaces and another my ultimate desired design.

Spaces I need to control: https://clone2-musicofnature.mystagingwebsite.com/wp-content/uploads/2019/07/spaces-to-reduce.png

Ultimate desired design: https://clone2-musicofnature.mystag...t/uploads/2019/07/ultimate-desired-design.png

 

Here are urls for two pngs:

Spaces I need to control: https://clone2-musicofnature.mystagingwebsite.com/wp-content/uploads/2019/07/spaces-to-reduce.png

Ultimate desired design: https://clone2-musicofnature.mystag...t/uploads/2019/07/ultimate-desired-design.png

 

Totally wonderful ... thanks so much!

And now another request ... In the metadata area, I only want the date shown, as in the "desired" design I sent you (remove author and number of comments). Can that be done with CSS? Or does it require php?

After that is tweaked, I assume I will then be able style the metadata text using the customizer.

p.s. One other option, perhaps more feasible, is to simply remove all the metadata. I'm actually not sure is any of that information is highly relevant because my content is "evergreen" and it doesn't really matter if people see that information in the archives.

 

Is this the correct CSS for reducing space above the post block, but only for archive pages? Or is there a better way to do it?:

/**divi.help archive - reduce space directly above posts area**/

.archive #main-content .container {
padding-top: 24px;
}

You can see it in action here:

https://clone2-musicofnature.mystagingwebsite.com/category/podcasts/

The code reduces the space between my search field and the post area below it.