If you want to show some content from one site collection on another, the RSS Feed Viewer Web Part is an easy way to overcome the restrictions MSFT has put in place. The only caveat is the source content must be hosted on the public side of your account. Feeds of internal content (team sites) will not work.In this example I’ll show you how easy it is to display a list of blog posts from one 365 site on a site in a completely different site collection. This is how it will look:
Activate the rss feed in the list/library settings
Open the list and copy the rss feed url (click the rss icon to get it)
Open the page you want to display the list on
Insert an Rss Feed Viewer Web Part
In the web part properties, paste in the rss feed url
That’s it! Now you can display 365 list/library content on any other site – even a site external to 365. You can see an example here»
One neat thing about the viewer web part is that when you click a list item title, an excerpt will open in a drop down with a “see more” link to the full content. A feed of a document library will show a selection of fields in the drop down-though I’m not sure how to control what shows. Users with appropriate permissions can also click through to find a link to open/download the document.
As you can see, my example is on a public site, which by default doesn’t include the RSS web part. No problem, you can either download it from your team site’s settings» web part gallery or from here».
Then, since access to the public site web part gallery is “hidden”, append /_catalogs/wp/Forms/AllItems.aspx to your domain and upload the web part.