No, push and in-app notifications will come from your app. They don't have any dependency on the Facebook app. People who receive your push campaigns don't need a Facebook account or have the Facebook app on their device in order to receive your push or in-app notifications.
Not at this time, but you can target push campaigns based on platforms, devices, app events (either pre-defined app events or custom ones you might have created) as well as parameters on your app events.
Performance limitations can occur when creating segments. There can be a delay between a few minutes to several hours depending on how many past events must be reprocessed in order to build the new segment.
See the “Segment Processing Time” section in the Overview section for more information. Depending on how many devices are eligible for a particular push campaign, the processing time for a campaign to be scheduled and sent can range from immediate to a few minutes.
In-app notifications currently support images and animated GIFs, along with an optional JSON payload.
Yes, you can include a deep link to in your push campaigns that opens a specific experience in your app. Also, in-app notifications feature buttons that can deep link within your app or link to an external website.
Yes you can add parameters to both deep links and web URLs on any external links you include in your campaigns.
Yes, you can add your own custom JSON data to your push campaigns.
Due to a change in the way iOS 10 handles push notifications, the current Push quickstart documentation is not accurate for iOS 10. We are aware of this issue and are in the process of updating the documentation. For additional details, along with a description of the work-around, see the related Stackoverflow discussion at http://stackoverflow.com/questions/39382852/didreceiveremotenotification-not-called-ios-10.