Remove the width and height values, or just the height value, from the tag.

Q1: Can I change this at once for all images in all articles on the website?

Not with JCE. You would need to edit each article individually and remove the width and height values or attributes. You could try RegularLabs DB Replacer - https://regularlabs.com/dbreplacer - to perfom a search/replace of the article content to remove the width and height attributes, but you need the "Pro" version to do this properly, using a regular expression.

Why is this happening on this website, because on other websites it works fine? Could it be that I need to adjust a configuration in JCE?

Usually, the template has some css to make images responsive, even if they have width and height attributes set, eg:

img {
    max-width: 100%;
    height: auto;
}

but this website does not appear to have this. You could add this to your template css file, and it might solve the problem, without the need to remove the attributes from all images. You can also configure JCE to not add the width and height when inserting an image, by setting the Always Include Dimensions option to No in Editor Profiles -> Plugin Parameters -> Image Manager Extended.

Is the setting: Always Include Dimensions recommended as the default setting?

The default used to be off, but including dimensions on images is now recomended for better page rendering, especially on mobile devices where the image night take time to load, the layout is preserved during loading.