You are underestimating acceleration. To travel and come to a stop at 4.2 light years, a spaceship with 1g acceleration barely needs 3.5 years in relativistic ship time (~6 years earth time).
The technology to sustain 1g acceleration through 3.5 years is a different story, but very much within our understanding of physics (and not warp drives, etc). 20-50 years of engineering can get us there.
I want to believe, but I think it'll be a lot more than that. The rocket equation is a stone cold bitch in this case.
Sustaining the thrust that accelerates a probe at 1g is very different to sustaining the thrust to move the probe and all the fuel. And it's much worse if you want to stop and not just fly past into deep space.
It might not be. Plenty of hydrogen around everywhere. We just need tech to use it.
Our moon landing missions had a similar ratio, so I assume we can do the engineering to make even a slightly worse ratio work for us a 100 years after it.
In practice it would be better with slingshot maneuvers and picking up mass on the way.
What energy source do you think is merely 20-50 years of engineering effort away from being able to power that kind of journey?
Make it collide with stuff colliding with the ship, redirect it's energy for propulsion.
My point is that we are in the realm of just needing new engineering (how to make nuclear reactions, or even antimatter-matter collision work for this goal), not new science (warp drives, something else we don't understand about space or gravity, or mass).