1. What is conductivity? Is it the same as TDS?
"Electrical conductivity tells us how well a material will allow electricity to travel through it."
A conductivity meter has a pair of electrodes with a space between them. They are submerged in the water and a small current is sent out of one electrode. How much reaches the other other electrode determines the conductivity of the water. As noted pure water is a poor conductor.
Conductivity is usually measured in micro- or millisiemens per centimeter (uS/cm or mS/cm).
"TDS stands for total dissolved solids, and represents the total concentration of dissolved substances in water. TDS is made up of inorganic salts, as well as a small amount of organic matter. Common inorganic salts that can be found in water include calcium, magnesium, potassium and sodium, which are all cations, and carbonates, nitrates, bicarbonates, chlorides and sulfates, which are all anions. Cations are positively charged ions and anions are negatively charged ions."
Note that nitrite and nitrate etc. are ions and they contribute to conductivity/TDS.
TDS are similar to conductivity, A TDS meter is basically a conductivity meter which uses a formula to convert the micro-siemens into ppms.
I have a continuous monitor on a tank. It gives the choice between using a reading of Conductivity or either of two different formulas for TDS. I can make sense of ppm easier then micro-siemens so I set it for TDS.
Bear in mind the conductivity/TDS tells us nothing about what exactly the water contains. It only gives one a good Idea of how much stuiff in total is there.
2. Does low conductivity related to low pH?
Usually this is the case. But then lower pH also relates to soft water. Soft water means there is less stuff in it. However, this is not a 1 to 1 relationshsip. You can have different levels of conductivity at any given pH reading. But the general rule is they are both similar- low pH and lower conductivity and higher pH and higher conductivity usually go together.
3. Is poor mineral content the same as low conductivity?
Basically, yes. Simply put. "A mineral is a naturally occurring inorganic solid, with a definite chemical composition, and an ordered atomic arrangement." So that is a lot of what is dissolved in water.