You would need to design in at least two screen sizes (unless you know exactly how layouts would scale): desktop/laptop and mobile. You may need to add other screens such as tablet and TV, depending on the requirements.
As for the measurements of the elements (or lengths), assuming you will use CSS, you can use either fixed (eg. 100px) or dynamic (eg. 10vw) value. Within the fixed measurements you can use either absolute (eg. 12px) or relative (eg. 0.75rem) value. Normally you'd mix all of these in your CSS and set them depending on the screen size using media queries so that the layout adopts to the different viewports. So, you need to discuss with your developer to set the responsive design strategy first.
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