Outlook Inbox Won't Keep Messages

[MF@18th]

I have a new HP Pavilion x360 laptop. I subscribed to Office 365 to get Outlook so I could bring my Spectrum Webmail (@roadrunner.com) emails into the Outlook program and read them there.

My Outlook has two problems:

1. It will only show emails received today. Anything older disappears. I cannot look at any emails I received in past days, weeks, months, or years.

2. When a new email arrives, even the earlier ones from today disappear. I can find no way to retrieve them and get to see them again.

I talked with the tech support people at Spectrum. They say the problem is with Outlook. I talked with the Microsoft tech support people also. They say the problem is with the Spectrum server.

I would very much appreciate any light you can shed on this situation. Thanks in advance for whatever you might be able to tell me