Attached here is a console test application that can be used to test Autodiscover, Impersonation and PullNotifications for Exchange 2010 and above as well as Exchange hosted/Online

 To make a test do following:
-Unzip the ExchangeTestApp.zip attachment and enter test and service account details in ExchangeTestApp.exe.config file – replacing the XXXXXXXX values  and eventually true/false values of other attributes.
-Run the exe and observe results (url and your calendar entries) and wait until you see the message “Press a key to exit”.
- Application will create a number of txt/log files at the installation directory and we will need to check them only if you get the error while running this app.

About Autodiscover
It might happened that this application gives correct result when you run it from your machine but you still have issues with Autodiscover. In that case run this app from the server where your solution is deployed and check the results again.
You might need to add/correct DNS CNAME or SRV record for Autodiscover.

For Exchange Online, Microsoft expects a CNAME record for Autodiscover. Host Name: autodiscover, Target: autodiscover.outlook.com

If you use default Office 365 domain, the one with ‘onmicrosoft.com’ you probably don’t need to create extra DNS entries.
For custom Office 365 domain, e.g. 'office365.company.com' there needs to be a CNAME record created for the service address space 'office365.company.com' that points to 'autodiscover.outlook.com'.
You may need to add the fully qualified domain name as your hostname, e.g. if your domain is 'office365.company.com' your hostname would be 'autodiscover.office365.company.com' instead of 'autodiscover'

If you have both internal and external DNS records then they both have to be configured correctly for Autodiscover to work properly. It is recommended to create CNAME or SRV record in both internal and external DNS.

Note that SRV Autodiscover though a valuable record for an on premise environment (i.e. _autodiscover._tcp.domainname.com), it appears that it is not a required DNS record for Office 365.