Nope, sorry. Undergraduate statistical mechanics--see e.g.
Cosmic background radiation is very, very faint--which is why it's hard to measure.
Right, which is one good way of proving that the curves can't cross--if they could, you could just use an optical filter and make energy flow spontaneously from cold to hot--which would be a perpetual motion machine.
Antennas are commonly tuned by pointing them at the sun and adjusting for maximum signal at the desired frequency--see e.g.
Not so. See above.
The difference there is that their angular subtense is so very small--in the picoradians or smaller, something like 10**-23 steradians. If you made an antenna big enough that a quasar, say, could fill its entire beam width, you would indeed get a big fat signal, bigger than if you pointed the same antenna at a star. The problem is that such an antenna would be the size of the Milky Way, or thereabouts.
Cheers,
Phil Hobbs