Here's the bottom line, they aren't going to bother spying on you because that ends up costing money...they would just get rid of you if they thought something was up (unless it came to corporate security). Those policies are in place for the BYOD generation and there's not really a sure fire way around it without risking leaks.
My technicians know that if they leave my company their devices will be remotely wiped if they do so without warning and agree to it in the employee handbook before they even begin work. We have SSN, Credit Card Information, Contacts, etc that are accessible at any time. If they leave with a two week notice then they are allowed to backup their personal data and then wipe the device in front of someone authorized to verify it - it's not that we want that policy, it's because we HAVE to have that in place for liability sake. Can you imagine the CEO of a Multi-Billion dollar business contacting you when a term'ed employee uses a SSN/CC to go shopping?
You CAN set permissions on your work calendar. You can make it to where if you set your appointments details to private that others around you can't see the details (only that you aren't there). You're lucky to be able to access both calendars on site like that because most corporations wouldn't allow it (it's too easy to just start migrating data over, that's the risk).
In the end, everything is visible when it flows through the backbone. If you access it from home, your details will become visible because more than likely you'll be proxying into the server to access said accounts (especially with Exchange 2013). If you're really THAT cautious, ask your employer for another device that purely carries your work data and nothing else, that prevents a BYOD scenario.
EDIT: EndPoint Management means that we can see your screens without you knowing. HTTPS means zero if you're linked in to the network.
That is exactly what we do here at my company. Sure we can do all of that and more but that costs us time and money. We truly don't care what is on your BYOD device...we care about maintaining the integrity of the corporate data. The same goes for what is on the computer. That is why each and every employee agrees to the acceptable use policy/cisp when they are hired. That is also why the BYOD program isn't all that popular...most are very happy with a corporate provided phone. Those that do use the BYOD program are told very clearly that we DO not do a full device wipe but rather an enterprise wipe...thus leaving their personal data intact. The AUP/cisp clearly states that all usage on the corporate network is subject to monitoring...including personal email accounts.