Tilt Social Share Widget allows your users to quickly share your content on social sites. View "Description" tab for available services.
Yes. You can apply your own CSS to the icons. If you don't style it and don't use the Tilt Social Share CSS, the widget will gracefully fall into your site's Unordered List classes.
In the settings form, there's a field labeled 'Order', which you can use to achieve your desired order. By default, the order shown in the settings is the order followed, but the slugs inside the 'Order' field will appear primarily followed by the other active share services.