To answer your questions, those little rectangular parts are capacitors, you're right. They are small value caps, and would probably be ceramic caps if replaced today. The two coils you're referring to are intermediate frequency (IF) coils. They, along with those caps, resonate at an intermediate frequency.

Your radio uses a superhetrodyne circuit, which is the most modern type and uses IF amplification stages. The Superhetrodyne receiver circuit was invented in 1918 and most radios were made that way from about the 1930's on. In a superhetrodyne radio, the RF signal is converted to an intermediate frequency for most stages of amplification. That way the IF amps can be tuned to a specific frequency and optimized for it. The RF section has to be wideband, since it has a tuner and covers a large frequency range. So amplification is not as efficient as the IF stages, which operate at a single frequency. The IF stages are where most of the gain is done, and then the IF detector converts it to audio for the final audio amplification stage.