OP - regarding expansion of the universe, try reading about Hubble's Law and the Hubble constant. In short, the redshift of light (caused by space expanding) from distant galaxies is proportional to their distance. From our point of view on the Earth, distant galaxies appear to be moving away faster than nearer galaxies. (This may seem somewhat of an Earth-centric definition but it's our only vantage point. On a large scale, the universe appears to be pretty much isotropic, i.e. uniform in all directions, so if you were standing on a planet in some far away galaxy, you'd still see the same expansion.)
The balloon example is a good one if, as one poster noted, you use "sprinkles" instead of Sharpie dots. Another analogy is raisin bread. Start with a generally homogeneous lump of dough (analogous to space) and raisins (analogous to galaxies), cook it and it expands to a homogeneous loaf of raisin bread (analogous to an expanding universe). The dough expands and not the raisins (they may, but here the analogy fails). Moreover, the raisins (and dough) at the outer parts of the loaf expanded more rapidly than the raisins in the inner parts.
Space between galaxies is expanding, not the galaxies themselves (unless caused by other means like galaxy collisions.) Galaxies - collections of billions of stars - are gravitationally constrained, that is, gravity holds them together. Clusters of galaxies - collections of tens to thousands of individual galaxies - are assumed to be assumed to be gravitationally constrained too. Our own Local Group of 40+ galaxies, while not generally considered to be a galaxy cluster though there is no absolute line between a "group" and a "cluster", is contracting. Light from galaxies in the Local Group, of which the Milky Way and Andromeda are the biggies, is blue shifted from our perspective.
So "when cosmologists and astronomers speak of the expansion of the universe", they are generally referring to space between galaxies, and not galaxy clusters or the individual stars, planets, atoms etc which make up a galaxy. In gravitationally constrained systems, the strength of gravity far exceeds any expansion (if any) of space within the system. This is fortunate for life on earth. Our solar system is gravitationally constrained which is why the earth, Mars, Jupiter etc aren't all receding from the sun. Moreover, like other galaxies, our own is held together by gravity; the solar system is not leaving the Milky Way.
In the 20th century, cosmologists and astronomers discovered that universe threw us a couple of curve balls, namely dark matter and dark energy but no one knows what they really are!
Galaxies rotate, and the angular velocity of outer stars should be enough to cause them to fly away from the galaxy, but they don't. Some unknown source of gravity is holding them together. Hence the term dark matter - we can't see it anywhere in the EM spectrum but we can observe its effects. (There are other theories too.)
The standard cosmological model of the universe has the universe expanding ever since the Big Bang. Most models include some form of extreme expansion (called inflation) right after the Big Bang, but that lasted only 10^-35 seconds or so. Studies of type Ia supernova in distant galaxies in 1998 revealed a big surprise; not only is the universe expanding, but about 5 billion years ago, the expansion began to accelerate. Other studies have confirmed this observation (though, like dark matter, there are other theories.)
Finally, a meter stick can indeed contract (besides thermal contraction/expansion.) It's the Lorentz contraction which Einstein incorporated in his Special Theory of Relativity. However, the definition of a meter remains constant as does the speed of light (in vacuo.) Fortunately, we don't have to redefine the length of a meter every time we measure the speed of light travelling from one medium to another.