FIRST QUESTION
If we go back to the basics:
Boyle's law says that for a fixed mass of gas the Pressure x Volume is constant if temperature is constant.
This means that if we half the pressure we will double the volume. But doubling the volume means that the same mass is of air fills twice the volume. This will half the density. So each time we half the pressure we half the density
If we go from ISA mean sea level to 35000 ft, the pressure falls from 1013.25 mb to about 218 mb. This means that the pressure at 35000 ft is 218/1013.25 = 21.5% of its mean sea level value. So if temperature had remained constant, the density at 35000 ft would be about 21.5% of its sea level value. This represents a 78.5% reduction in density.
But as altitude increases, the temperature decreases. So we must also consider the effect of this temperature decrease.
Charles' Law says that Volume / Temperature is constant if pressure is constant. This means that if we half the temperature we will half the volume. This will double the density.
But Charles was talking about the absolute temperature not the temperature in degrees Celsius.
At ISA msl the temperature is about 15 degrees Celsius, which is 288 degrees Kelvin. This reduces by about 2 degrees for each 1000 ft increase in altitude. So at 35000 ft the absolute temperature is 288 -(35 x 2) = 218 degrees Kelvin. So the temperature at 35000 ft is 218/288 = 75.7% of its sea level value.
This means that if the pressure had remained constant the density of the air would have increased to 1/0.757 = 1.32 of its sea level value. That is a 32% increase in density.
So as we climb from ISA msl to 35000 ft the reducing pressure tends to reduce density by about 78.5% while the reducing temperature tends to increase density by about 32%.
From these figures it can be seen that the reducing pressure is the more powerful effect. So as altitude increases the air density decreases.
SECOND QUESTION
If we increase temperature at any given elevation, the air will expand. This will reduce its density.
The air will tend to expand in all directions, but downward expansion will be limited by the surface of the earth. So the majority of the expansion will be outwards and upwards. This means that as the temperature increases at any given elevation, the upward expansion of the air will increase the mass of air that is above that elevation. Static pressure at a given elevation is caused by the weight of the air above, being pulled down by gravity. So by increasing the mass of air that is above a given elevation, increased temperature will increase the static pressure at that elevation.
So increasing temperature at any given elevation will decrease the density and increase the pressure. It is this increased static pressure which causes altimeters to under read when the temperature is above ISA, and to over read when temperatures are below ISA.