I removed blinkfeed as my homescreen but it still running in the background and draining my battery. How do I stop it from running and/or delete it?
you cant delete it but you should be able to disable it through your settings-apps.
BTW, it can no longer be disabled in 4.4.3 on the M8. I imagine the M7 will be the same when you receive it. So to get around it, make sure you do a Clear Data and Clear cache after removing from your homescreen. This will delete any settings for news feeds, social feeds, etc.. and prevent it trying to update.
As Fireguy mentioned though, you should still be able to disable it through Manage Apps > All tab and search for Blinkfeed. Basically, same place you would go to Delete Cache or Data for an App.