The lift is equal to the weight of the displaced air. The net lift is the difference between the weight of the air, and the weight of the helium displacing it.
Air has a density of about 1.2 kg / m3, and helium has a density of about 1/7th of that. The lift of a balloon (ignoring the mass of the balloon) is therefore about 1 kg / m3.
Barometric pressure and air temperature play a small role, since
$$PV=nRT$$
from which you can derive that the density will go down with higher temperature, and up with higher pressure. But the changes are typically just a few %.
As for the rate of ascent - this is typically limited by the drag of the balloon(s). Hard to estimate this, but drag for a sphere goes with the square of the velocity: this means you need 4x greater lift force to go twice as fast - but that means a 4x greater volume of balloon, which will have a greater area... Greater lift speed would best be achieved by using a pear-shaped balloon. In fact, for high altitude ballooning (think Felix Baumgartner's jump from the edge of space) you start with a balloon that is heavily _under_inflated as the helium will expand at higher altitudes (lower pressure). What is interesting is that the lift will be the same if you allow the balloon to expand - so the lift really is a multiple of the mass of the helium (in a ratio of about 6 to 1).
You would need approximately 17 kg of He to lift a 100 kg load (including the weight of the balloon etc).
I) But haven't masses in vacuum not the same attraction and speed.
No. Their weights are different, so they are not "attracted" / pulled in by gravity equally.
Think of this: If you find 100 heavy perfectly round stones, and you put 5 plastic balls full of air with exactly the same size in the basket with them, what will then happen when you shake them a bit? Will the lighter plastic balls fall to the bottom or "float" to the top?
They will float to the top.
The point simply is that it is easier for helium atoms to move up than for air molecules. If you shake the basket violently, the stones might jump a bit while the plastic balls can jump much higher. So on average, the helium atoms will move much higher upwards, and as soon as they do that, some oxygen molecules will take their previous location. Now they have a new location higher up, and the same happens.
Overall this causes the effect of buoyancy, sometimes called updrift, which is the force that this lighter material is pushed up with. And this upwards force is exactly the same as the force, with which the heavier materials pulls downwards - in other words, the lighter material is pushed up with the weight of the displaced heavier material, which now pushes to come back in place.
This was Archimedes' discovery.
Now to your other sub-questions:
Can be said that for airmolecules the atmosphere is a vacuum?
Well, no, a vacuum is a vacuum. If there are molecules present, it isn't vacuum, and the atmosphere isn't a vacuum.
So all together helium should have the same attraction to earth as the other airmolecules?
No, their "attraction" to Earth are different, because that "attraction" must be weight. And the helium atoms weight is lower.
II) Because helium atoms are much lighter, perhaps they could have a higher speed than fe O2 or N2?
Mass (or weight) doesn't influence possible speed. It only influences how hard it is to make them reach the speed.
Ok, but those helium atoms are in a balloon so they pushes at all sides of the balloon equal so the balloon shouldn't move at all?
If only the balloon with helium was present, and no gravity or outside atmosphere, then you are completely correct. The inside pressure cannot make the balloon move. But with gravity present, the whole thing is pulled downwards, and with the atmosphere present, there is a buoyancy force upwards as discussed above. Which-ever of these forces is greater, makes the balloon move.
III) When a balloon starts ascending from the ground there is more air (pressure) above him than beneath. So the airpressure above him should push the balloon to the ground?
Incorrect. You actually said it yourself just before: Inside the balloon, the pressure equalizes throughout so the push at any point on the balloon is the same. Same goes for this air column: All the air in the column above presses down, but the tiny bit of air below pushes up with the same force to balance out the pressure.
Best Answer
Helium balloons are pulled by gravity, as are all objects with mass. The reason they don't fall is that there is another force acting on them, a buoyant force from air pressure that is equal to the weight of the air displaced by the balloon.
The reason you don't float is that the weight of the air you displace is quite a bit less than your weight (a person is more dense than air). The reason a normal balloon doesn't float is that the weight of the air it displaces is just a little bit less than the weight of the balloon (because it is filled with air, but the rubber of the balloon itself is more dense than the air).
The analogy you want is to objects floating (or suspended) in water. Most rocks sink to the bottom, pulled by gravity, because the weight of the water they displace is less than their own weight. A bowling ball (ironically) is very close to the same density as water, so it will float suspended in mid-water, just like the helium balloon that has leaked a little bit.