As far as I know, there have been several attempts to reverse engineer the WhatsApp Android application itself, but not with focus on WhatsApp Web and, more importantly, often not in the context of FOSS.

In general, WhatsApp Web actually needs the phone, as WhatsApp messages are stored only there. WA Web just uses the WA servers as relays, which pass requests like "give me the last few messages from this contact" to the phone. In the end, the private (Signal Protocol) keys are stored on the phone and are supposed to never leave it. That's why creating an entirely FOSS client for WhatsApp would need a complete rewrite of the Android application for desktops/platform independent as well.

If you use genymotion you can forgo the cellphone. Though the SMS must be received somehow and the qr is also an issue

Related: #10
For the moment I am using the Android app on my Linux computer with Anbox (and using Android x86 on VirtualBox with the extension pack for webcam support to scan the QR code).