Thank you for your interest
I don't have Outlook in my pc, i have outlook.com, that is i go to
www.outlook.com to manage my mail. I don't know if that answers to the "what kind of email you are using" question.
On the other hand, in my phone i have, as you said, the mail app - which is quite poor, in my opinion. I guess if i want to do what i describe in this thread, i will have to access my mail through the browser, something strange to me, since i would expect from Microsoft to give more complete integration - unless i am missing something.
Yes you've answered the question and now I have a better understanding of where you are. So I'm not certain what level of understanding you have of your phone so please don't be insulted if I give directions on how to get to things.
So you are using an Outlook.com. The only syncing you want to achieve is between the two. Now obviously the functionality on the phone will be slightly different than the web version but you should be able to see the same information.
Now I don't know if the Outlook.com email is your MS Account or not but I'm going to assume it isn't but will tell you the difference if there is one.
1. Go to Settings -> email + accounts -> Tap Outlook account -> set Download new content -> as items arrive. If you want all your past items on your phone you can change Download email from -> any time
2. Under the above settings you have Content to sync. These are check boxes, you can set which ones you want to sync here. (If this is your MS Account you will only have Email)
3. You can force a sync by doing a long press on the Outlook account and pressing Sync
Now go into your Outlook email on your phone.
If you have folders you have to set the sync for each folder individually.
1. To find your folders press the ... then folders
2. Select folder you want
3. Press sync this folder
4. Folders will have the same sync setting as the account so if you don't want everything showing up for that folder change the sync setting under Press ... Settings -> Sync setting before you sync it.
Calendar and tasks (different app than email)
Your calendar and tasks should automatically sync if you have those checkmarks as indicated above. If this is your MS Account it will sync automatically and you can only change this in setting in the calendar.
To setup what you see in the calendar do the following:
1. Open the Calendar app
2. Press ... Settings -> then turn on and off things you want
3. At the bottom you'll see Preferences, check the boxes of things you want
Hope this helps you out.