You need to have the full serial number including "egg" in the URL for the dashboard, i.e.: https://airqualityegg.wickeddevice.com/dashboard/#/egg/egg00802d945f9b0102
You can also download data from your Egg in CSV format from https://airqualityegg.wickeddevice.com/download by filling in the form and specifying a period of time to download. You can also upload CSV data acquired in this way to an online plotting tool we developed at https://airqualityegg.wickeddevice.com/multiplot
The other URLs you suggested are defunct for the moment. We're doing a bunch of work over the next couple of months to unify the tools and data experience. I don't have on my radar at the moment an embed-able widget, but would be happy to hear your suggestion about what you might like to see in this respect and we can see what we can do to support that. Best would be to email suggestions like that to support at wickeddevice dot com.
We are working on making this more accessible.
