First off, it looks like you might have posted the wrong chunk of code for your second error.
The error was “has exactly one input with a name of ‘pet_name’ and an associated label with the content ‘Name’”, but I see that you posted code related to the email. I can take a look if you re-post the pet name section.
As for the first error, it looks like you have set the width to 100%, with a max-width of 600px in the media screen, which should do the trick. I would recommend going back and looking at your code / testing in your browser to make sure that you still meet the other requirement, that the form elements are the width of the screen when the screen is less than 600px wide. Is there something you could add to the top form element that would allow it to be be narrower if the screen was narrower?
It is actually possible to meet both of these specifications without using a media screen, but it is also possible to do them with media screens as well. That’s the beauty of programming - there are often many possible solutions.