To setup anonymous text chat with random strangers go here:
https://strangermeetup.com/
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To setup a ZELLO account to make voice chats like walkie-talkies go here:
http://www.zello.com

You will always need an Internet connection for this to work. Someone should set up a Zello group like HACKADAY - CONFERENCE or something. After you make a free Zello account you advertise your Zello name on your badge website.

 Zello is a stand-alone app for your PC or smartphone. It can not be seamlessly part of your website. It will work in the background while you are using website though.

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To make an anonymous website that is a international service in Germany, with an Italian domain name, and run by a Polish kid in Poland go here and set up a link there and use it as your quasi-website. It accepts HTML tagging, hyperlinks, formatting, password protection, etc:

https://justpaste.it/

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Here is a QR Code reader for your smartphone:
https://play.google.com/store/apps/details?id=me.scan.android.client&hl=en

Here is a QR Code maker to make paper signs, badges, or T-Shirt iron-on:
http://www.qr-code-generator.com/

T-Shirt Iron Ons:
https://www.google.com/search?q=t-shirt+iron+ons&ie=utf-8&oe=utf-8

Here is how to make laminated ID badge with lanyard: