There isn’t a definite answer “when” someone has to crop images. Some people want all the images to have the same size and some people don’t.
I personally find it easier to crop images using a photo editing software before uploading or use WordPress media for manual cropping so I get to choose the area to be cropped.
Images should be responsive unless they are background images. Unfortunately I can’t quite tell why it isn’t working for you without seeing the site live.
You can send it through the Contact form here to keep it private if you wish:
Let me know 🙂