Irreversible reactions

Because they are no longer available for reacting. Assuming the gas has very little solubility in the solution, once it forms it will bubble out and diffuse into the atmosphere.

The precipitate is a bit trickier but not really. When a solution is in contact with a precipitate the interaction between solvent (or whatever solutes may be present) and the solid occurs at the interface of the phases. That is only the exposed layer of solid will ever get to see the solvent or solutes. You can demonstrate this to yourself by dissolving equal masses of sugar in water but using sugar cubes versus confectioner's sugar (or regular powdered sugar, or all three). You'll quickly notice the different behaviors and should be able to relate this back to your situation.

You can also try and read up about an abstract concept called chemical potential, which can be used to, more rigorously, describe such behavior as my answer is just quick, dirty and intuitive.

 

Then you have to use thermodynamics make some reasonable predictions about the system. If the free energy of the process favors some sort of equilibrium you will have a mixture of products, reactants and gases.

 

Not necessarily, it only means that the product is not soluble and is therefore not in the actual solution.

Consider it this way, a completely made up case:

A_(aq) + B_(aq) ⇔ C_(aq) : Keq ~1

C_(s) ⇔ C_(aq) : Ksp ~ 10^-10

The low solubility of C_(aq) will force the reaction to proceed very much further than the equilibrium constant may lead you to believe. If we ignore the solubility of C, we would expect [C]_(aq)/([A]_(aq)(aq)) ~ 1. However because the solubility is so low the solution never actually gets enough [C]_(aq) to get to ~1 because as far as the solution is concerned there is very little C_(aq) around (it precipitates out and becomes C_(s)). Only a thin layer at the solid/solution interface is accessible to A or B, effectively small enough to be considered negligible. So the reaction proceeds to make some more C_(aq) which precipitates out. So on and so forth.