Does Outlook.com provides any webhook/push-notification support?

seems to work fine No hook that I'm aware of, but you could run all of your pushes through one place in your code (either client or a cloud function), and do whatever post-push work you want to do there. Presuming JS and advanced targeting, it could look like this:

function pushToInstallations(query, data) {
    var params = { where: query, data: data};
    return Parse.Push.send(params).then(function() {
        // this is the interesting part, run the installation query
        return query.find();
    }).then(function(installations) {
        var date = new Date();
        // presumes underscore, but a regular for loop works too
        _.each(installations, function(installation) {
            installation.set("mostRecentPushDate", date);
        });
        return Parse.Object.saveAll(installations);
    });
}

var query = new Parse.Query(Parse.Installation);
query.equalTo('someColumn', someValue);

pushToInstallations(query, {alert: "some message"}).then(function(installations) {
    // these installations passed back were pushed to and updated
}, function(error) {
    // handle error
});

This might help you Thank you for reporting this issue. Microsoft engineering team is investigating it right now. Meanwhile, a workaround that worked for multiple subscription cases is to use relative URL for the resource property
e.g.

wish help you to fix your issue To subscribe the notification of other calendars, you need to change the the "Resource" to "me/calendars/{calendar_id}/events".
GET https://outlook.office.com/api/v2.0/me/calendars

{
  "@odata.type": "#Microsoft.OutlookServices.PushSubscription",
  "Resource": "me/calendars/{calendar_id}/events",
  "NotificationURL": "...",
  "ChangeType": "Created, Updated, Deleted"
}

With these it helps The Webhooks are only supported for user level credentials. i.e Each user has to give the app a permission to request data on behalf of users. However, in our case, we need to get notifications for all user emails to reach our application and this is impossible to do at the time of writing (Sep 2016).
The solution we went forward is to build a batch job to pull all data. An Admin has to give an access to the application (the application will have its own identity) and make subsequent requests. For the app to identify itself, we have used X.509 certificate

fixed the issue. Will look into that further The ViewAction mentioned in the payload is not supported now. You should replace it with OpenUri action. you can find more information about in our documentation: https://docs.microsoft.com/en-us/outlook/actionable-messages/card-reference
Please use the following payload and it should work fine.

{
"title": "New Office 365 Group: Success",
"text": "Performed by: someuser",
"themeColor": "00e600",
"sections": [{
        "title": "Section Title"
    }, {
        "facts": [{
                "name": "Name",
                "value": "PRJ000001"
            }
        ]
    }, {
        "potentialAction": [
            {
                "@context": "http://schema.org",
                "@type": "OpenUri",
                "name": "View Log",
                "targets": [{
                        "os": "default",
                        "uri": "http://..."
                    }
                ]
            }
        ]
    }
]
}