I want to know how long is the longest lifespan a red dwarf star can ever have? Also, I want to know the approximate percentage of red dwarf stars that can live for trillions of years.
Models of stellar evolution suggest that the lowest mass red dwarfs (about 8% the mass of the Sun, these are the smallest objects that can fuse hydrogen) can last for something like 10 trillion years. Red dwarfs are usually defined to be stars with less than about half the mass of the Sun. At about a quarter the mass of the Sun a star becomes completely convective, so the gas in the star circulates all the way from the core to the outer envelope, whereas stars like our Sun only have a region near the surface that is convective. Being completely convective means that the star can access, and burn, all of its hydrogen reserves whereas stars like our Sun will still have significant amounts of hydrogen when they leave the main sequence and die. This, combined with the decrease in the speed at which a star fuses hydrogen as it decreases in mass, means there is thought to be a jump in lifetime at about 25-30% the mass of the Sun to over a trillion years. More than half of all red dwarfs probably fall into this mass range and so will likely live for over a trillion years. Incidentally these completely convective stars will also never become red giants, but will simply gradually run out of nuclear fuel and transition directly into white dwarfs.
Bear in mind however that there is considerable uncertainty in these estimates since the present age of the Universe is about 13.5 billion years, which means there has simply not yet been time for any star with a mass less than about 80% that of the Sun to complete its evolution. As such we cannot observe any red dwarfs in these advanced stages of their lives to check whether our models are correct.