Hi there,
Thanks for writing in! You need to set your site to a content + Sidebar layout to get a sidebar for the blog index page and sub-pages.
Appearance > Customize > Layout and Design > Layout Content >> Select Content Left, Sidebar Right or Sidebar Left, Content Right.
For the rest of the site which you would like to be fullwidth, you will need to select a fullwidth page template.
Edit Page > Page Attribute > Template >> Select Layout – Fullwidth.
or
Edit Page in Cornerstonte > Settings Tab > General > Page Template >> Select Layout – Fullwidth.
Regarding the social Icons in the header area, they are there by default, just turn on the top bar.
Appearance > Customize > Header > Miscellaneous > Topbar >> Select On.
Hope this helps – thanks!