These are some pretty hard questions for a non-physicist like me.
But there is a simple difference between photons and protons:
Photons are quanta of electromagnetic radiation (in one word: light) so they have no intrinsic weight and will travel with light speed; that's what they do.
Protons are "stuff": in fact, more half of all matter around us (including you and me) consists of protons. So a near light speed proton is not much different from a bullet, only a wee bit faster.
Hope this helps.
About the double slit experiment: I'll leave that to the professionals.
Anything unrelated to the LHC