Even after I heat and oil, why does food stick to my stainless steel pan?
Stainless steel pans are not non-stick by default, since they don't have a non-stick surface/coating.
You can recognize a non-stick pan by the non-stick coating on the inside of it. (It's usually Teflon (a black coating), but there's also things like ceramic)
As far as your pan goes, it looks like a plain stainless steel pan to me, no coating to make it non-stick.