I'll let others focus on plausible alternative bio-chemistry configurations, but I wanted to do my best to explain to you why our biochemistry works so well. The first thing you need to know is that bio-chemistry is all about energy release.
Let's start with the basic food that all living things need; carbohydrates. These are Carbon, Hydrogen and Oxygen. What do these three elements do? Well (and this is a bit of a simplification but functionally correct) the hydrogen provides energy, which the oxygen releases, and carbon allows our cells to combine molecules in many different configurations to either store or release energy.
Carbon based life forms are possible because Carbon is a relatively simple element that can connect to multiple different elements simultaneously to form complex molecules. Water is essential for life because it's an extremely stable molecule (H2O) which stores the two primary elements needed to generate energy. Water is (quite literally) rocket fuel stored in its lowest energy state.
Now we get into endothermic v. exothermic reactions. All these words really mean is that chemical reactions can either consume energy (endothermic) or release energy (exothermic). Photosynthesis is an endothermic reaction. It takes CO2 and H2O, both low energy state molecules, applies sunlight to transform them into O2 and Carbohydrates, which are higher energy state molecules.
Plants (and animals) get their energy by consuming the carbohydrates, mixing them with O2 so that they revert to their lower energy states (CO2 & H2O), keeping the released energy for themselves.
The important thing to note here is that ALL these chemical elements are relatively simple, and relatively common in the universe as a result. From a physics perspective, you have to remember that our current theories tell us that the only element that existed in the early universe was Hydrogen, which gets converted via fusion in the heart of stars into heavier elements. The heavier the element, the bigger the star required and therefore the more rare its going to be (again, a simplification but functionally accurate).
So, while things like silicon have been suggested as alternative bases for life, they're less likely because it's a heavier element than carbon. Again, this area I'll leave for people better qualified than I to explain.
Regarding your questions about flora, the answer is probably no. Plants on earth exist because they can use photosynthesis to generate the critical molecules for their own use, but they still need water to do that. Additionally, plants need soil (not just for water but) for the complex minerals that they extract from it. They also rely on many different microscopic bacterial functions occurring in the soil, without which they cannot grow themselves. Soil (as opposed to rock) can absorb water, see minerals shifted around inside through bacterial functions, and provide a medium in which roots can grow without having to split the rock to do so. Sodium Chloride (NaCl, also known as salt) isn't an alternative energy source to water; it's hydroscopic (meaning that it reacts with water and stores it) which is why salt can be useful to life.
With regards to plants making other chemical molecules required to breathe in non-carbon based life forms; this is possible but would still require an endothermic reaction. The reaction (like in plants) would have to produce an excess of the life giving molecules, which get released as a 'waste' gas.
Mind you, if that was the case, it's possible that some form of mobile life form (for now let's call it an animal) may also be capable of photosynthesis in some form, or geo-synthesis (using geothermal heat to generate the same effect) or some other form of energy capture.
Ultimately, I suspect that if we do find extra-terrestrial life out there it's likely to be carbon based purely because of the availability of the elements required (probability) and the simpler chemical reactions required to get it going (efficiency). Either way, don't get hung up on Earth based life and the distinctions we have between plants and animals. Any life form capable of storing energy in chemical form through an endothermic reaction could lead to a diverse ecosystem on its home planet.
