When the air/diesel fuel mixture is compressed, the process is nearly adiabatic so the temperature increases. When it gets hot enough, it ignites. The increase in temperature comes from the work done on the mixture as it is compressed (1st law). Not all the energy from the burning fuel can be utilized to move the piston back out and turn the crankshaft (2nd law).
Not exactly. The first law of thermodynamics, i.e. the law of conservation of energy, also accounts for heat as one of the many forms that energy can take. There is no one law called "the law of thermodynamics", but there are several "Laws of Thermodynamics" (note the plural form "LAWS").
Biology is immune from the laws of thermodynamics because biology has a higher law, a superior principle, the submission of all to Evolution, from which flows a continual stream of order and, when necessary, heat.
Thermodynamic cycle is based on 2nd law of thermodynamics.
The 1st Law of thermodynamics is a restatement of the law of conservation of energy.
Magic
The first law of thermodynamics is also known as the Law of Energy Conservation.
Entropy is closely related to the 2nd law of thermodynamics, not the 1st law. The 1st law of thermodynamics states that energy cannot be created or destroyed, only transferred or converted. Entropy, on the other hand, is a measure of the disorder or randomness of a system, which increases over time according to the 2nd law of thermodynamics.
"Unavailable for doing work" is related to the Second Law of Thermodynamics.
That law is known as the Law of Conservation of Energy. It is also known as the First Law of Thermodynamics.
The first law of thermodynamics states that energy cannot be created or destroyed in an isolated system; it can only change forms. This law is also known as the Law of Conservation of Energy.
You didn't specify what you mean with "the following".To the best of our knowledge, conservation of energy ALWAYS applies. There are no known cases when you can create energy out of nothing, or simply make it disappear.
There is no commonly accepted law by that name, as far as I know. Two important laws about energy are the First Law of Thermodynamics and the Second Law of Thermodynamics.