If space works as a balloon then the growth happens in all the volume of the universe (not just on the “boundary”). Is that how it works? Doesn’t that imply that we are getting “bigger”?
However, at scales so large that gravitational attraction has attenuated to nothing, this repulsive component of gravity is still getting stronger. At the scale of galaxy clusters, it is pushing everything in the universe apart in all directions: faster the farther apart they are. At a certain distance, it becomes so strong that objects will appear to be moving away from you faster than the speed of light.
The distance at which that happens is called your Cosmological Horizon, and it has similarities to the event horizon of a black hole turned inside out. Unlike a black hole, however, there isn't a single unique event horizon. Every distinct gravitationally-bound object (galaxy cluster) in the universe has its own cosmological horizon; every other object is being pushed out towards it, and vice versa.
I think this just opens more questions than it resolves, and would really like to hear a better explanation.
(In fact space inside galaxies isn't expanding at all, only space between galaxies. But I digress.)
It's when you measure between one side of the observable universe to the oposite side that the expansion speeds get crazy.
Yes, if by "we" you means "large scale cosmological structures".
But galaxies stay roughly constant size because gravity holds them together. Smaller things are also held together by various forces.