Yes, its built in with native code, but it will use your website URL to show your websites inside the app.
Usually each app is finished in 2 - 3 working days.
No, it does not please contact us for the source code, it costs $800 for the source code.
Yes, it can support One Signal service push notifications, please note its an additional service, which will cost extra based on the type of your website.
For App store, it will cost extra of $100 for publishing into App Store. It will take 3 - 4 working days to finish publishing once all information is received.
It will cost only $50 for the play store publishing. It will take 2 - 3 working days to finish publishing once all information is received.
If you provide a local HTML folder, yes. If your web content is hosted on a website, then it will only work if website is online or user has internet access.