Helmet out of EVA foam

Hello, i am new to cosplay in general, first time working with EVA and Pepakura. I am making a base of a helmet from "Outer Wilds". I have a few problems i`m not sure i'm understanding right.

1. On Pepakura there`s visible a lot of gaps, i understand that they needed for assembly, though i don`t really know what how to close them. Glue them together? -- I`m afraid the helmet shape will change and will appear compressed. My best guess is to use either cutout EVA for every gap, or to use some caulking compound. Also i know my model is very far from perfect, but its the best what i can get.

2. Is this even possible? There`s seem so many pieces that i`m not sure it`s sane idea to do something like this.

Thank you for reading, and any help is welcome. Sorry if the post turnes out to be silly.