Does every photosynthetic organism including microorganisms have the ability to switch from C3 to C4 pathway under stress (water scarcity, high temperature etc.)?
Eleocharis vivipara can switch from C3 to C4 photosynthesis when transferred from aquatic medium to terrestrial medium (or when ABA is added into aquatic medium). Besides this, Hydrilla verticillata is known to switch from C3 to C4 photosynthesis under adverse environmental conditions. There are many papers about these two species that can be found in the literature. These two species are the ones that I know, there may be other examples. Hope this helps!
"C3 plants" (called C3 because the first STABLE product of carbon fixation is a C3 molecule) have chloroplasts in their mesophyll and not their bundle shealth. They suffer from photorespiration on hot dry days. "C4 plants" have chloroplasts in both cells; the bundle shealth has RuBP, but the mesophyll has a different binding molecule (PEP) with a higher affinity for CO2. So, PEP (a C3 molecule) can bind CO2 at low concentrations, and then the product (a C4 product) is passed to the bundle shealth. In the bundle shealth the CO2 is dissociated from PEP, and PEP is returned to the mesophyll. This keeps the concentration of CO2 in the bundle shealth high enough for RuBP to keep fixing CO2, even though the leaf may be closed. So, PEP "pumps" CO2 into the bundle shealth, keeping the concentration of CO2 high enough that photosynthesis (and not photorespiration) will occur. This allows C4 plants to maintain glucose production even on hot dry days when their stomates are closed. Grasses are classic C4 plants, and they have adapted physiologically (and morphologically) to their environment.
You provided an explanation on how the C4 plants could be more efficient in water management in "This allows C4 plants to maintain glucose production even on hot dry days when their stomates are closed." but I believe that it was more accurate if you used "slightly open stomata" or "more closed stomata". This is because someone may wonder about how the plants can fix CO2 with closed stomata.
It is well known that the PEP Carboxylase enzyme which is responsible for initial fixation of CO2 in mesophyll cells of C4 Plants has much more affinity to CO2 than RubisCO. Therefore the C4 plants can extract CO2 more effectively from the entering air via stomata (down to near zero concentrations of CO2). This is why they can do the same amount of photosynthesis with half opened stomata than that of a C3 plant can do with full open stomata. They need less air circulation via stomata to supply their CO2 need. This is why some C4 types could be more resistant to drought and have more water use eficiency in general. However, remember that the process of non Photosynthetic CO2 fixation (CO2 fixation via PEP carboxylase to Oxalate, Mallate and Pyruvate cycle), consumes some energy as ATP. Therefore the C4 plants would be winner in climatic situations that they can trade-off this extra used energy with an advantage like resistance to drought and/or higher temperature .
This is a wild assumption. A few plants transiently tide over the adverse situation for a limited period of time; otherwise no plants will die when climate adversely affects them.
In C3, C4 or even CAM for that matter, besides enzyme machinery, anatomy too plays a crucial role in photosynthetic carbon fixation. In fact no plant is fully empowered with all the three modes of carbon fixation