There are multiple different variations, options, sizes and text questions that can be used at an individual product level. All of these options can be accessed via the individual product's Options/Sizes tab.
You can also append an inquiry form to all your products. From your shopping cart manager select Setup > Display Options > then tick the checkbox labelled "Include an enquiry form" then click[Save]
Additional question fields and file uploads can be entered in at the checkout page, but those questions are fixed to the entire order, and are not product specific.
If you are working with events, consider using our events management system, then adding generic products within that area that can be connected to your events.