How to properly set up an outlook.com account on Android
 

Gmail supports Exchange, but insists on using IMAP. Exchange supports PUSH and more options. Should work with hotmail.com and live.* too.

From settings select Add Account then Exchange.
Enter your user name, but select Manual Setup instead of Next.
Enter your password and change Server to eas.outlook.com.
Account is ready, but I recommend these:
In account settings, change Sync Frequency to Automatic (push).
Enable extra folders in Folder Sync Settings. Change Sync emails from.
Your Name is ignored, set that up from outlook.com web mail.

I just use the Outlook App from Google Play store.

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I find it interesting that my emails show up faster on my phone using the Outlook app than they do on my computer running Outlook. It is very consistent. I keep my phone near my computer and know an email will soon be coming in on the computer when the phone notification sounds.

I thought you had a FastMail account? And if so I'm curious why you elect to use the Outlook app on your phone as opposed to using FastMail (app) with a mail fetch identity set up to the Outlook account? Is it just because of the extra time new Outlook messages appear in FastMail or some other reason?

I use the Outlook.com app for my Microsoft business account. I have various email systems for various things. I find the best experience if you use the app from the company that supplies the email: Gmail app with Gmail, Outlook app with Microsoft, Fastmail app with Fastmail, etc.

I use the App to check Junk for misplaced emails. One thing that I at first disliked was "All Accounts". I have three accounts. I wasn't sure I was seeing all the emails. Now that I am sure "All Accounts" works, it a nice quick look to see if any account has something in Junk. My normal use is via an email client on my computer to download emails from the three accounts I have using POP3.

Same here. If the service has an App, I use it.

Normal use case for the App is to check Junk or Spam. as I POP3 all but a couple of my accounts. With these POP3 accounts I do any reply, forward or new messages using my client on this computer. For those IMAP accounts it doesn't matter as every thing is on the server.

I don`t use the MS Outlook app because it`s bloated. I don`t want mail/calendar/contacts integration. I don't want two different email apps. All the AI is confusing for casual users, I disable it in Gmail. I tried it when it came out, and it filled my contacts with everyone I received email from.

For people who use the Microsoft services more than Google's, it makes sense. I don't.