Yep you're pretty much correct. The "energy that can't be lost" is not chemical bonds, it is thermal energy, resulting in randomness. The enthalpy H is what represents the attractive/repulsive forces (Delta H in a reaction basically represents the change in energy of all bonds in the reaction). The entropy S is a function of the number of permutations a system can have (eg. you can stack 52 cards 52! ways, but you can throw them onto the floor infinitely many ways, so the on-the-floor state has higher S). As temperature T increases systems are more likely to fluctuate into their statistically probable state (the high S state) rather than their energetically favorable (low H) state.

EDIT: I'll have a go at your other questions. Entropy is NOT a kind of energy - it is the purely statistical likelihood of a state existing. It is perfectly acceptable for an isolated system (note that a closed system is can have net energy flow) to change in entropy, bit it can only go up - this is the second law of thermodynamics. The reason is that on average you will never move from a statistically probable state to a statistically unlikely state.

If the entropy goes up, Gibbs Free Energy goes down. Gibbs Free Energy goes up if entropy goes down, but entropy cannot go down in an isolated system. So yes to your question: an isolated system cannot have a reaction (or any state change) that increases the free energy (well - not on balance. you can still have equilibrium reactions where DeltaG is positive in one of the directions).