Shopify's default contact page and form feature only allows you to collect basic fields, including name, email and message.
Even if you edit the HTML and Liquid code and additional form fields appear on the form, the data in these fields typically will not be collected properly.
You should always test any custom form code to ensure all fields you need are properly collected and stored before you start using the form as, once users start submitting the form, any information in the non-compatible fields will not be collected or stored and there is now way to retrieve it.
If you need to collect more information from users, you will need to use a third party form app or form tool.
If you need to add custom fields to products, please see this article about line item properties, which are different than contact forms.
One downside of Google Forms, however, is that, while you can control the color scheme of the form, you cannot customize fonts, remove the Google branding or change other design elements. The data collected by the form also cannot be directly feed into Shopify's custom database.
If you need more advance form functionality including more control over the design or integration with Shopify's customer database, you may want to check out some of these apps.
However, please note that because these apps are developed by third parties, we're generally not able to provide any guidance on which would be the best fit for you or assistance with installation or technical issues. We also cannot guarantee they will work with our themes. You'd need to contact the app developer directly with any questions or support required.