The population declines that are observable now are very small in relation to the whole population, it's usually 0.1-1%. Population is declining the fastest in the lower class, so not much value is being inherited, and it shouldn't cause a price inflation because it also lowers the demand for goods.
The lower class population are the biggest consumer and this contributes a lot in my opinion.
I don't think so, I have never see a chart where the lower class is the biggest consumer on this case, coz if we talk about the purchase power it would obviously be on the upper class population. We can't conclude this just because the lower class population is bigger than those above.
But inflation isn't the only thing that you should be worried about, and population decline can have other negative or maybe even positive consequences (opinions of economists here can vary).
I agree that there are other factors when it comes to inflation, I think the decrease is just one of them, remember the hyperinflation of German mark after World War 1, the war reparations took a toll to the masses of Germany, and in a sense, losing a war for conquest is a big factor for inflation.
With growing population in the world, and inflation I think these two are relative to each other somewhere coz the inflation is powered by demand especially when the economy of a developing country is rapidly moving upwards, so the more the people the more it would cause inflation. When the population decreases, the inflation won't remain, it may just be slowed.