Few things from quantum mechanics are needed to explain this: 1. Pauli exclusion principle, no two electron can occupy a same state. 2. Band theory of solids. There is an energy gap in the density of states in semiconductors and insulators, but none for metals. 3. And then that conduction can be explained by scattering from occupied states to unoccupied.
What it essentially means that electrons are free is that there is "plenty of room" for an electron from occupied valence band to scatter to a very close by unoccupied state (in conduction band). There are no such "close-by" states available in an insulator, so the conductivity will be very poor.
Now for your question about charging an insulator. Yes, it works. You have essentially reinvented the doping of semiconductors, resulting into development of transistors. The only practical difference is that it is impossible to charge an insulator to required charge (and the charge would probably be at the surface only). However, by introducing defects into an insulator/semiconductor one can effectively charge the conduction band with electrons (or remove electrons from valence band with other types of defects). This happends in finite temperatures, since the defects are easily ionized and donating electrons. And here, the system will remain electrically neutral, since the defects are charged positively and they donated their negative electrons to the conduction band. There is room for electrons in the conduction band to scatter to empty conduction band states and conductance is increased.
There is also intrinsic semiconductivity, where no doping is required, and there also, the conduction band is "thermally chared".
Get together a collection of charges. As many different ways to generate a charge as you can think of. Go ahead and invite your friends so they can think of some more. (As a practical matter you make static charges just before you use them, but still...)
Now, test them pair wise to see if they attract or repel one-another. Keep careful records.
Find the largest set that are all mutually attractive and the largest set that are all mutually repulsive.
You'll find that the attractive set has exactly two members (though you can make many different examples of this set) and the repulsive set consists of half (either half!) the charges you've created.
Ponder that for a while. It also gives you the answer to how like charges respond to one another (though you can get that directly by preparing two similar charges).
Best Answer
Adhesion between different materials can result in a transfer of electrons between the two materials.
This is the reason for bodies gaining net charges after they have been in contact with one another - charging by friction.
Different substances have different affinities for electrons but to predict which substance will gain/lose electrons is very difficult and it is the empirical results which are usually quoted as a triboelectric table.
Your balloon although a good insulator in the bulk might have surface moisture on its surface and as water is a relatively good conductor in electrostatics experiments some of the charge might leak away by conduction through the water.
Although the air is a good insulator there are charged particles (ions and electrons) in the air which may originate from dust, air blown over a wet surface, hot bodies/flames, natural radioactivity and cosmic rays. These charges in the air will neutralise the charges which are on the balloon.
Feynman has a chapter in his book entitled Electricity in the Atmosphere which will give you some more information.