What is a false wall and what ways can I have my subs mounted?

This is probably the most basic style of boot installation there is ( other than a plain box installed into the boot) 
A false wall essentially is creating a panel that seals off a section of the boot so you can only see the walling face and everything up to it. Installs can have hidden equipment behind a false wall such as Airbag suspension setup, Amp racks, Storage, Sub-woofer enclosure etc. 
This can be useful to neaten off a boot by walling in a sub-woofer enclosure to create a neat and tidy install. 

Flush Mounted, Flat Mounted, Rear Mounted, Reverse Mounted

This term is used to describe an objects/speakers mounting styles or possibilities. A speaker or sub-woofer or object can be mounted to a panel in a number of ways. 
These change the way something looks and can be used to hide screws and mounting brackets for a stealthy look.

Flush Mounting

When an object is flush mounted the top of the object is flush with the surround surface. This is typically used in subwoofer and speaker installations so you have a flat section where the speaker or woofer can be indented without protruding outwards.  Notice how the subwoofer surround is flush with the yellow front trim panel so it is essentially embedded into the box, this is known as flush mounting

Flat Mounting

When an object is flat mounted the object is simply mounted directly to the surrounding surface. This mounting method means the object, in this case the sub-woofer, is protruding outwards on the surround.  Notice how the subwoofer surround Steps outwards and isnt flush with the surrounding carpet on the front panel. This is known as flat mounting

Reverse Mounting

When an object is reverse mounted it is simply facing the opposite direction. This is typically used in sub-woofer installations as an aesthetic or to gain maximum box volume to increase peak in spl. Reverse mounting a sub-woofer can increase sub-woofer noise as the air that passes over the basket, can result in added unwanted noise. In this case, mounting a sub-woofer so the magnet is visible outside the box is known as reverse mounting.

Rear Mounting

When an object is Rear mounted the surround of the object is mounted behind the face that is visible. This is typically used in sub-woofer and speaker installations so you have no visible mounting points or screws.  Notice how the sub-woofer has no visible screws holding it as the surround is mounted behind the front panel. This is known as rear mounting