The first kit is a hearing aid circuit (補聴器キット Hochōki kit).
As you probably guessed, the circuit captures sounds through a microphone and amplifies them with a transistor. The user with hearing problems listens to them through headphones.
The second kit is a Tesla coil plasma speaker (テスラ電光音発生器 Tesura denkō-on hassei-ki). By the way, there are now other Tesla kits with larger coils.
This circuit is somewhat more complicated to explain. Basically, it is a high-frequency oscillator that accumulates energy in the coil. The oscillator wave is amplitude modulated by another input wave, for example, music. Bringing a screwdriver to one end of the coil produces an electric arc discharge and makes noise. That noise when modulated by the song turns the coil into a speaker.
It is best to see it with your own eyes. Watch the video I recorded.
You can also use the kit to light a fluorescent lamp.