Here you need to customize one of our layout to make it identical with your competitor website. Please make sure to copy one of our layout to your wordpress theme from Wp Masonry > Layouts. Once you copy it, you get the new location of the theme and can customize it. Doing this it will be safe from future updates as well.
For equal height and width of the images, you can use same height images for your post. Or you can use this function (https://developer.wordpress.org/reference/functions/add_image_size/) and define your self a new image size. Don’t forget to set crop as true. This will force croping the image in exact dimension. And then you can select same thumbnail size while creating shortcode.
Regarding the layout they are using, those are from other themes or plugin. So it is not available in our theme.
PS: Really sorry here but we are currently unable to take any theme customization. We are busy with some other commitments.