Featured Image on the left in the blog post

Hi there,

Something like this should help you to get started:

.blog.separate-containers .inside-article,
.archive.separate-containers .inside-article {
    display: flex;
    align-items: center;
}

You would need the Content Template feature from GP Premium to replicate the exact layout in your example screenshot.

You can try something like this:

.blog.separate-containers .inside-article .entry-header, 
.archive.separate-containers .inside-article .entry-header {
    width: 75%;
}
.blog.separate-containers .inside-article .post-image, 
.archive.separate-containers .inside-article .post-image {
    width: 25%;
}

Please be mindful that the purpose of this free theme support forum is to assist with free theme features and not to provide CSS solutions.

Your requests so far can all be achieved with GP Premium:
https://generatepress.com/premium/

Thanks for your understanding 🙂

I then search options to show categories and change their design. But could not find any.

The options are included in the blog module of GP Premium:
https://docs.generatepress.com/article/blog-content-layout/

I get the feeling that you are trying to replicate the layout seen here:
https://snipboard.io/yFQlZn.jpg

And as mentioned above, you will need the content template from GP Premium to do so:
https://docs.generatepress.com/article/block-element-content-template/

We cannot help with full custom CSS solutions in this free theme support forum.

Thanks for your understanding.