Good questions, and: cherish that curiosity!
On 1: An object you can toss into the air is generally a solid and generally contains of the order of 10
20 to 26 atoms or molecules. In a solid the molecules are fairly close huddled up, bound by some force, most of the time electromagnetic. This maintains the shape of the object so much we can threat it as if it were, well, an object. We deal with it in a macroscopic way: weight, position, orientation, velocity, temperature.
Air is a gas, meaning the forces between the molecules are smaller and the average distances between them a lot greater. They move about at high speed and collide zillions of times per second (it is very instructive to calculate average speeds, speed distributions, number of collisions per time, per volume etcetera). Sometimes we think to know that the speed is dependent on temperature, but in fact it's the other way around. Pressure has to do with the number of molecular collisions, be it among each other or against the walls of a container, or an object tossed into the air: molecules, all of them.
For the subject at hand you can treat these collisions as hard-ball collisions, which on a molecular scale they are to a great extent, but on a submolecular scale they are not. They are spring-like interactions that change the trajectories of the particles involved. Far too many to worry about. Especially when the size differences between the colliding participants are of the order of magnitude of > 10
6, let alone of the order of magnitude of the number above.
In a (imaginary) hard-ball, head on collision of two equal billiard balls with exactly equal speed, there is an indivisible moment both have speed 0. The kinetic energy is zero, but since we believe in conservation of energy, it must be somewhere else. Going from colliding blocks of butter, via rubber balls to hard balls, we can convince ourselves that it's been converted to energy in compression, a kind of energy as stored in a compressed spring. Spring energy is re-converted into kinetic energy by expansion force and re-appears as kinetic energy, ideally without losses. The billiard balls have swapped all momentum. Ideally.
You could say that the balls have stopped, but under an imaginary submolecular microscope the shuddering and shaking of the molecules in the solids has not stopped at all: there is no dropping of the temperature to absolute zero, therefore motion must have continued.
There is no concept of stopping when dealing with molecules. Changing speed, direction of motion, slowing them down, ok.
Now think of the collision between an ideally hard billiard ball and an ideally hard wrecking ball, again head on. Billiard ball at high speed and wrecking ball hangs still. Do you think one could notice the effect on the big guy? No way. Momentum differences after and before are imperceptible. Not zero though!
But that imperceptible effect increases if we start firing thousands of billiard balls per second at the wreching ball. At least it wouldn't hang completely vertical from its chain any more.
Wikipedia has nice gif animations of brownian motion
http://en.wikipedia.org/wiki/Brownian_motion
that are a beautiful intermediate step between molecules among themselves and an object tossed up in the air. (Note that the pictures do NOT have gravity).
5 molecules, dust speck, grain of salt, coin, billiard ball form a sequence of objects that 'feel' relatively less and less of individual collisions with molecules. Not only because of the bigger and bigger weight, also because of the area: they get hit more and more frequently
from all sides.
Someone like you was curious enough to wonder about the chaotic motions of pollen in water under a microscope and had the effect named after him. Someone else did some quantitative work on this and it now counts as confirmation of the existence of molecules. He became the most famous scientist of all times!
Back to our wrecking ball in a gas of billiard balls.
Hanging still: collisions from all sides, average net result zero. But wait, gravity makes air pressure height dependent! So a bit more from below than from above. Eureka! In the passing we've come by Archimedes' discovery as well: in a vacuum the chain tension would be a little higher than in air.
Throwing it up means the 10 to the umpteenth molecules bound together have an average speed upwards. More collisions from above than from below. There's what we call the air resistance in supra-molecular circumstances. Dust takes longer to settle than a cloud of wrecking balls...;-) Do I have the sensation of Galilei enthousiastically nodding his head ?
Bottom line: there is a lot of exchange of momentum
on the fly. Newton's third law in action! 'Object' behaviour is determined by averages over 10^many collisions that have almost no effect on object (but the individual air molecules experience a ruddy hard collison with a pretty hard rubber wall). No stopping.
On 2. You are absolutely right. Same thing. I have a hard time imagining what you mean with "a wire with a ball connected to the edge and spin it ". But yes, as the world turns, we don't fly off into space in a straight line because Earth and we attract each other. (Newton 3 again!). That's a force vector, perpendicular to the velocity. It doesn't change the speed, only the direction of the velocity.
As an feeble attempt at humour: If the population on one half of the world jumps up at the same time, the Earth moves a little in the other direction. Not for long, but still. However, the center of gravity of world + population) follows the same path as in the case nothing happened.
