Can eternal inflation and gravity explain dark energy? First of all, I have absolutely no background in astronomy and physics. I just watch a lot of "i-hope-scientific" youtube channels talking about physics and astrophysics and I can kind of follow the maths and concepts.

So, I was thinking, with absolutely no physics to support this:

REAL QUESTION STARTS HERE:

Say, the big bang happened everywhere, followed by inflation that never stopped. This is wat eternal inflation described (if i am correct)

Then, as eternal inflation goes on and more and more universe outside of the observable universe is created. Then there would be an unlimited amount of mass outside our observable universe. 

Can this mass create an gravitational effect on the galaxies in our universe?

We are at the center of our observable universe, so the gravitational effect of all the mass outside our observable universe would never affects us. But from the perspective of another galaxy, it would be affected by a bit of universe that is outside our observable universe. 

Then you might explain the effect that galaxies that are farther away from us move faster away from us. And that galaxies closer to use move slower away. Then you can explain this by saying that the galaxies farther away are closer to the "unlimited" mass outside our observable universe. And thus are more affected by this. And that galaxies close by are less affected.

The theory with dark energy claims that dark energy causes an outward push from the inside of our universe. Wouldn't this be indistinguishable from a gravitational pull from the outside?

Also, could this explain the red-shift we see in light from the far end of the observable universe? If I remember correct, gravity can red-shift light if the light moves away from the source of the gravitational pull (as seen near black holes). Light form the far end of the universe has moved trough the gravitational pull away from the "infinite mass" of the outside universe.

This was my idea, and I would like to see where I am thinking wrong.

One thing where I obviously might be thinking wrong is that this effect would be homogeneous throughout the universe and it should cancel out. But is this also true when you throw some relativity into the mix?
We need to cover some basic concepts: inflation in our universe ended 13 billion years ago. Inflation occurred for just a short period of time after the big bang. Eternal inflation is different. It hypothesises that spacetime is infinite and keeps on inflating. In some regions of spacetime, the inflation stops and the energy from this inflation is converted into energy and matter. This region where inflation stopped becomes sort of like a 'bubble' in the ever inflating spacetime. This bubble is then a universe. This there can be multiple universes accelerating to this hypothesis.
Okay. Our current theory of gravity is General Relativity, and for now all you need to know is that it seats that gratuity thanks time to propogate and has only a finite reach unlike Newton's description of gravity.
So even if our neighboring galaxies have a slightly different observable universe, the gravity from galaxies far apart don't even affecter them at all. In fact, that is why or universe is expansion by without any noticable obstruction from gravity.
Gravity takes time to propagate and has a limited access, so far away galaxies don't even affecter each other. That is why expansion is actually happening.
Another thing is I think your understanding of dark energy is somewhat misleading. You say that dark energy pushes the universe from the inside. That is the exclamation it the universe. The expansion does not happen because of dark energy. Dark energy accelerates the expansion. We have observed that expansion of the universe is getting faster and faster as time passes. For this you need energy. That energy is dark energy, failed so because we haven't detected it yet.