Could we build a Dyson spheres around our planet? Would this give use enough energy coming from outside to engineer a full ecosystem?
A dyson sphere not around a source of radiation such as a star would be be there for energy gathering purposes. Some names for such a thing are shell worlds
1 - No we can't. See the rocket equation and available rocket technologies. Even if we could build rockets that are as reusable as airliners it would still be too expensive to launch billions of tons of stuff into space, just from the volume of fuels / oxygen that would need to be consumed.
2 - With current solar panel technology (~20% efficiency)we only need one Spain worth of solar panels to generate 100% of our energy needs from solar. In practice in the world there are enough constructed area so all we need is to use existing buildings / houses. At most perhaps install solar panels where it would be useful, like over parking lots to provide shade in the summer.
3 - If we cover all of earth with a Dyson sphere, it would be dark 24x7 here. Not a good idea.
A Dyson sphere is a scientific curiosity. We don't have a practical solution to build one. And it will likely take several hundred years worth of technological development to even conceive of a tiny / partial sphere that would perhaps orbit the sun not too far from earth and could be moved further out in the distant future as the Sun starts to expand as it shifts from fusing hydrogen into fusing helium.
A Dyson Sphere around the planet Earth doesn't make any sense. The whole concept is to build one around the sun, with a diameter that is about the same as the diameter of the Earth's orbit around the sun. It would involve using the mass of many of the planets to build the sphere and would replace the Earth with the inside of the sphere.
The whole point is to capture the entire output of the star to meet your energy needs and we are along way from needing - or being able to use - that much energy.
You do not seem to grasp what a Dyson Sphere is. It is a hypothetical structure that completely contains a star. There would be no energy coming in from the outside, no energy leaking out from within.
Short answer: We are at least many hundreds of years, if not thousands of years away from such engineering abilities. The relatively small ISS cost $150 billion dollars, and it is only the size of a small house.