As there are some extra options for notifications on each platform, Is there any option to set them?

When creating INotification instance with NotificationBuilder (via CreateNotification), you can set iOS properties with SetIosProperties and android properties with SetAndroidProperties methods.

On Android, How to make sure the notifications get a new entry for each delivered notification in the notification center dashboard?

You can make use of Tag property while setting the android specific properties when creating the notification.

On Android, Is it possible to show the notification even when the app is in foreground?

Yes. Just enable "Allow Notification Display when Foreground" property in Settings under Android section.

On Android, our server has different custom payload keys for title, tag and other standard keys. How to make the plugin work with the existing server setup?

It's possible to configure the payload keys of your choice in the plugin. Go to settings and set the payload keys as per your server setup.