Yes it does all add up - though it's not all totally intuitive, so maybe doesn't seem to add up.
1/ You're quite right carbon dioxide is heavier than air and so on a totally motionless planet not affected by any external or internal forces, over time the gases in the atmosphere might be expected to settle out into layers.
However the atmosphere is constantly under a whole range of forces mainly from the sun that produces our weather and so the CO2 is well mixed into the atmosphere and pretty evenly distributed.
The atmosphere consists of a VAST amount of air, so even billions of tons of CO2 doesn't push the actual portion up that
much. Unfortunately though CO2 is incredibly effective at being a greenhouse gas and so tiny amounts make big differences. The figure is closer to 0.04% - not 4%. There's also the fact that the oceans have been absorbing a lot of the CO2 produced, so all of that extra produced is not actually in the atmosphere.
The amount of carbon dioxide in the air certainly has increased in the last 20 years:
it has been doing so since the industrial revolution and is currently outside of any observed natural cycle:
2/ I don't know where you got your figures for car emmisions from, but some straightforwards if long winded calculations support other published figures.
The data is usually presented as mass of CO2 - not of just carbon. Working backwards from the figure of 135g/km of CO2 and assuming perfect combustion of octane (mostly what petrol is made of C8H18), this figure is equivalent to 59 miles per gallon, which is actually pretty optimistic, even accounting for some imperfect combustion!
1g of octane takes 3.5g of oxygen to burn it fully. This is 1 molecule of octane and 12.5 molecules of oxygen. This produces just over 3g of CO2 and 1.42g of water, respectively 8 and 9 molecules of each.
This is probably the counter-intuitive part in that 1g of a tangible substance (petrol - octane - an easily visible liquid) is producing more than 3g of CO2 an invisible, odourless, colourless gas. But the science all adds up correctly.
I've not completed any similar calculation myself before this, but it effectively means that for a petrol (gasoline) car, the mass of CO2 emmitted is 3 times the mass of petrol burnt!
Worth thinking about next time you're standing by the pump as all the fuel goes flooding into the cars tank!