Social media links are edited in 'Shared Connect' - under admin tools/footer - I think at bottom of list and it looks like a blank line in the menu. There was a problem in Picaflor's Responsive Sheffield Blue with editing these links - they turned to gobbedly gook and had to be changed directly in the database, but I don't recall having that problem in Winchester Black - should be able to edit them right in the tools menu.

The homepage slider is not same thing as Featured Products Carousel. The slides are defined in the banners manager. I'm not sure about removing the titles completely - I just customized to my own text. However I did vary the number of slides - the 5 dots in your screen shot indicate you have 5 slides active. Is this what you want/have your own custom images? If not you can turn them off in the banner manager main page - change status to red/off from green/on.

If the banner manager won't permit no-title, perhaps a short custom title that works with the slide content, or, find the css for the title and change color to transparent or display:none (?) Probably same for the dots if you want to keep multiple slides but no dots.