It's not clear from your post if you are supposed to be using an InDesign/InCopy workflow or not (I mean, if that's how you and your company do things). I'll guess not, since you seem mystified.
In that case, it sounds like you somehow inadvertently exported text frames to InCopy format. The InCopy export commands are about a half-inch above the Story Editor command in the Edit menu. I'm not quite sure how you could have done that accidentally, since the InCopy fly out menu looks quite diff. than the lone Story Editor menu choice.
Anyhoo…
The red circle icon is a feature of the InCopy workflow and it's telling you that the original ICML file (the exported InCopy file) to which that text frame is linked is now missing. You probably have a large text frame on each page, so it looks like the icon is for the page. You'll see the icon in the Links panel too. You get this if you move the ICML files or rename them or delete them, just as how it works with linked images.
To get rid of the red circle icons you just need to break the link(s) from the text frames on the page to the external ICML files. (The text in the InDesign file will remain intact and editable, don't worry.) The easiest way to break the link (for someone not familiar with the workflow) is to open the Links panel, select the ICML files — you can click a column header at the top to sort by status or type so they'll all group together — and then choose Unlink from the Links panel menu.
If there is a possibility that this INDD file is/was part of an InCopy workflow … maybe you're a new hire who stumbled into a production folder? … check w/the production manager or whoever before you do anything else.
AM
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