"What the front half of a jet engine (the intake/diffuser, and the compressor blades, i.e. all the stuff that happens before fuel is burned) does is; it heats up the air until it's hot enough for fuel to ignite" ...etc.
The heating up of air in the gas turbine cycle (Brayton cycle) is an UNDESIRABLE, but difficult to avoid consequence of the ideal gas law. A higher efficiency and power output would be possible if this heating did not occur, hence measures such as water injection or intercooling on large stationary gas turbines.
There are a number of other more subtle errors in the post.