Put an object in deep space which has been cooled down close to absolute zero. It will warm up- until it reaches equilibrium with the 3.2K cosmic background radiation.
A warmer object will cool down to that temperature.
Yes but no energy transfer is loss free, at least so far experimentally here on Earth.
The First Law of Thermodynamics requires that EVERY energy transfer is loss free.
Engineers might refer to energy that cannot be useful to, or contained by, their design as 'lost', but that's just taking a narrow view. The efficiency of an engine cannot be 100%; But the total energy in nevertheless always exactly equals the total energy out.
Some of that energy might leave the system about which the engineer cares, but none leaves the universe, and the physicist cares about the whole universe as a system.
'Leaving the universe' has no meaning. LOT, all three together , apply to a bounded system with inputs, outputs, and internal processes.
Could be a solar system or a refrigerator. At the level of cosmology and varying definitions of the universe, LOT can not apply. Applying LOT requires inputs, outputs, and doing work. LOT does not directly apply to cosmology.
Again you leaped before looking. LOT evolved in the 19th century from experiment and observation with steam engines.
1st Law always applies, but with qualifications. People tried to make perpetual motion machines based on 1LOT and they couldn't do it. Putting a generator on one end of a shaft and a motor on the other having the generator drive the motor is an electrical example of perpetual motion.
2LOT and 3LOT came about as qualifiers to 1LOT based on experiment. Matter and energy are conserved, but in a system all of the energy cannot be used to do work in the system. Take a look at the Clausius Statement.
The BB does not explain how the initial conditions came to be. BB is a good model, it accounts for all or most of observation today, but it is conjecture and extreme extrapolation back in time. Fitting LOT to cosmology is problematic. If the universe is finite, will it run down? My view is the universe in toto is itself perpetual motion ot infinite in energy.
The question of heat transfer by radiation between the background and an object can potentially be treated as a bounded system. Raising the temp of an object deducts energy from the background, which I believe is cooling. Then the boundary expands to the origins of the background. The boundary increases until it is bounded by a finite universe, or ecpands without limit in an infinite universe. That is my view.
The analysis of where waste heat goes is simple, if you understand LOT fully.
Draw a boundary around the Earth. A solar powered refrigerator creates waste heat. The heat is radiated away or conducted away into the ecosystem. Temperature rises. I'd have to look up the energy balan. . Solar radiation enters and powers the refrigerator. Thermal energy is added to the environment. The environment globally heats up, and some is radiated away into space. I don't know what the net thermal radiation is from Earth. Expand the boundary to the solar system, then the galaxy and so on. Eventually you run into what the bounds of the universe are, and that is what cosmologists think about.
The above is of course a sim-lification of climate science as to how wate energy moves through the ecosystem and what gets radiated away. That is what climatologists think about.
LOT is LOT engineering or science, that is why LOT is the foundation. It describes all workings short of cosmic limitations whatever they may be.