What is the ruling on refraining completely from speaking with the intention of worship, or to expiate a sin, or merely as a challenge, and is this considered an act of extremism?

Refraining from speech with the intention of worship is not permissible, as it is not mentioned in the Sharia, but rather explicitly forbidden. Al-Bukhari narrated from Ibn Abbas that the Prophet, peace and blessings be upon him, commanded Abu Isra'il to speak, seek shade, and sit, and to abandon his vow of silence and standing in the sun.

Likewise, refraining from speech as an expiation for sins is an innovation, because expiation is achieved through what Allah has legislated.

As for silence merely for amusement or challenge, it is permissible, as long as it does not lead to silence concerning a matter that ought to be spoken about. The Prophet, peace and blessings be upon him, encouraged speaking good or remaining silent. So if speech is good, one should speak; otherwise, one should remain silent.