On the specific event pages, I use the featured image as the only image on the event page.
– How do I remove the blue bar that runs along the bottom of that image? (the one that shows the name / date)
How can I remove the Google Calendar / iCal buttons from each event page?
It sounds like the blue bar you’ve described is unique to your theme. Would you mind sharing a link to the page in question here so I can have a look? From there I can show you how to hide it.
Do you wish to just hide the buttons with CSS (which is easy to do), or completely remove them from HTML (slightly more difficult)?