What is the pressure inside a closed bottle of air? Is it equal to atmospheric pressure? If so why? Surely the amount of air particles inside the bottle is much lower than the amount of the air particles above the bottle (i.e. the column of air above it) which should make it collapse as soon as the container gets sealed?
 A: Taking your argument about the column of air above the bottle and how it should crush it:
You are not getting crushed right now. Whilst you are correct that this will mean that lower down in the atmosphere there will be slightly higher pressure, it is essentially negligable compared to a few metres above the bottle.
Consider unbalanced forces, if the pressure in the bottle was substantially lower than the pressure outside, there would be an unbalanced force and the material of the bottle will accelerate inwards (you can see this in a cheap plastic bottle if you suck some of the air out).
A: 
What is the pressure inside a closed empty container (example: closed empty bottle)? Is it equal to atmospheric pressure? If so why?

Let's assume that you can completely empty the air inside a bottle and that you can seal it perfectly that no air from outside can enter. Then you would have a perfect vacuum in the bottle and the pressure would be essentially zero inside the bottle.

Doesn't the amount of air particles inside the bottle much lower than the amount of the air particles above the bottle (i.e. the column of air above it) which should make it collapse as soon as the container gets sealed?

Yes, for sure, the amount of air particles above the bottle (not only above but all around) and therefore the pressure outside the bottle will be higher than inside which would cause the bottle to collapse.
After answering your questions let me comment about this situation in practice. If you have a bottle which is not sealed then you have air inside and outside the bottle with equal pressures and everything is fine. If you close the lit and start pumping the air out from the bottle then the pressure will start to decrease and there would be some inward force on the surfaces of the bottle. If the bottle is plastic it would start getting smaller as soon as you start pumping. If it is a, say, glass bottle then it would resists the force for certain time and crack afterwards.
You can test this by putting the opening of a bottle in your mouth and suck the air into your lungs. If it is a plastic bottle if will immediately start shrinking but if it is a glass bottle nothing would happen because the glass bottle can resist the pressure difference that a human can create by his/her lungs.
