Does Feynman believe "the particle does not follow a single path but follows every possible path"?
Considering he's one of the people who pioneered the notion of a path integral, where you sum over all possible paths a quantum object can take to get from A to B, which is the corner stone of field theory, it would appear he does.
Then there's the diagrams which bear his name. If you want to compute say two electrons bouncing off one another you have to consider
ALL possible ways they can do this. First you consider them exchanging a photon only. That's how non-relativistic quantum mechanics says happen. But then you add quantum corrections, infinitely many of them. The first quantum correction is that the photon turns into a pair of charged particles (say an electron and a positron), they then recombine into a photon which hits the electron. Then you consider the next quantum corrections, that the pair of electrons created from the photon exchange a photon between themselves. Then you consider things like
that photon turning into a virtual pair and then back into a photon.
You consider
EVERY possible way the photon can get from the first electron to the second. Every possible circumstance, every possible energies and momenta the virtual pairs can have. Everything.
And it's that work which got Feynman a Physics Nobel Prize. And also QED is the more precise physics we have ever developed.
As Prom says, who should we listen to, someone who was considered one of the greatest physicists ever, who won a Nobel Prize, was renouned for his insight into the concepts of physics and whose textbooks give a complete description of the DSE, both qualitatively and quantitatively, which has been tested a great many times by a great many people, or should we listen to you, someone who doesn't know how science works, doesn't know any quantum mechanics or relativity but dismisses both of them and who doesn't realise if you're going to claim "I've explained gravity!" (as you did on PhysOrg) it means you must be able to accurately model physical systems using your work. Given I asked you many times to do that and you couldn't, you are lying when you make the afore mentioned claim.
Do you know any vector calculus, linear algebra or group theory? They are the backbone of all kinds of physics. If you don't know them you can never develop a viable model of gravity or understand the precise reasons QM explains the DSE in both a conceptual and quantitative way.
You make the mistake so many people do, mostly cranks, of thinking that because you find a concept doesn't square with your intuition it must be wrong. Your intuition is the result of being familiar with patterns of everyday life. Given quantum mechanics isn't the kind of thing which shows up in everyday life normally and you ardently avoid reading up on quantum mechanics you don't grasp it's concepts. And a 30 second Wikipedia read isn't enough. Those of us who
do have quantum mechanics coming up in our lives each and every day see how QM explains the DSE.