Hello,
Happy to assist with your query.
So what’s happening is that you are logged into your iphone’s Outlook app with your Hotmail account, it sends and receives properly, but mail from yesterday (August 20) to March 1 are missing.
Here’s what you need to do to get back those emails
The first step for any desync is to check if those items were moved to a folder, they may have been moved by mistake.
If they aren’t found to be in any folders check the deleted files folder, they may be in there.
If they still aren’t found you may need to resync your outlook app.
Go to your iphone’s settings, then mail, then mail accounts, then outlook, find your Hotmail account and tap there, in there you should be able to find “Mail days to sync”, go there then set it to “No Limit” It should sync your entire email history from including the gap starting from March 1.
If the emails still aren’t found you can try this as well.
In that same interface of mail accounts, you will need to delete account, make sure you remember your email and password before doing this as you will need to login again to restore your account. This should resync your emails and restore the missing emails.
For your second query, if you want your Hotmail mails to be sent to outlook you will need to get the outlook app from the Appstore, then open Outlook, and go through the “Add Account” process, you can have both the Mail app and Outlook active on your phone at the same time but it may be confusing, I suggest keeping the Hotmail account on only one app but that is just my personal preference, this is up to you.
Hope this helps,
Juan