philosophy of 1st law of thermodynamics Why is there heat emission/absorption when there's work done, at fixed internal energy ? This is a result of the 1st law, but I'm contemplating on the philosophical basis. Why does there have to be heat involved accompanying work done, when  internal energy is not changed? How do heat and work play together?
As an example, when pressing a solid hard keeping it at  the same temperature, the solid doesn't deform or move or change its temperature in the 1st place. As per the 1st law, the solid has to emit heat. But why does the pressing bring about  heat?
 A: Your question is not philosophical at all. It a is quite technical indeed.
It is true that the first principle says that a transformation at fixed internal energy implies that if work is done on the system, then heat should be released to the environment.
However your example of pressing a solid at fixed temperature is not a good example of a fixed energy transformation. 
The reason is that if temperature is fixed and a pressure is applied, the volume has to change in order some work is done on the system. And indeed isothermal compressibility of a solid, although small is a finite number. 
However, internal energy of a solid is not independent on the volume (deformation).
A relevant example would be an ideal gas kept at constant temperature. In that case, since $U$ depends only on $T$, the isothermal transformation is at constant $U$. 
However in such a case it is not misterious that the constraint of fixed temperature  (energy) implies a release of heat: an adiabatic compression would increase energy and temperature of the system. The condition of constant temperature is obtained by establishing a thermal contact between the system and a thermal reservoir, i.e. a big system at constant temperature. So, as soon the compression starts, the ideal gas would get warmer but thermal contact implies some heat release from the system to the reservoir.
