The Qur’an onlyists, claim that only holding onto an infallible source is both necessary and sufficient. Yet, they gloss over the fact that it was ‘fallible’ men who preserved the recitation, writing, and language of the Qur’an, with their ‘fallible’ memory, transmission, etc. The Qur’an onlyists are also of course, completely ignorant of the ahruf (modes of recitation), and would probably be unable to answer which ahruf is infallible (all ahruf are considered valid by Muslims). The transmission of the writing and recitation of the Qur’an, is what Muslims call mutawatir (mass transmitted), which leaves no doubt that what we have of the Qur’an, is indeed the same Qur’an that Prophet Muhammad (S) transmitted to his companions. What the Qur’an onlyists are especially unaware of, is that some Hadith are mutawatir, and such Hadith which are mutawatir in wording, are actually considered to be on the same level as the Qur’an.
To know the ahkam (derivation of rules and laws) would require having an extensive knowledge of the Qur’anic Arabic, its meanings, morphology, grammar, asbab al nuzul (occasions of revelation), nashk (occasions of abrogation), etc. which they don’t possess (neither do I).
Salah (prayer) and its different timings are indeed mentioned several times in the Qur’an (Surahs 2:238, 11:114, 17:78, 50:39).
So is Sawn (fasting) in the month of Ramadhan (Surah 2:183-185).
So too is Zakat (almsgiving) obligatory (Surahs 9:11, 73:20, 98:5).
And Hajj (the greater pilgrimage) too (Surahs 2:197, 3:96-97).
Here are a few more general verses which are relevant to this discussion- Surah 5:3, Surah 3:85, Surah 5:48, Surah 4:59, Surah 9:122, Surah 16:43 (this has a contrasted meaning when compared to Surah 21:7).
I have not heard that story.