In Sunni Islam, the Hadith is essentially a companion source to the Quran - in particular, Sahih Bukhari and Sahih Muslim.

But I should have been more specific. I think Shia art has the same restrictions though - could be wrong.

Islamic canon law (the Shariah) is derived from primary texts (the Quran and Hadith) and uses interpretive methodologies (like deductive analogy - Qiyas) to derive rulings that are not explicitly discussed in the primary source material. This gives some amount of openness and causes some differences of opinion resulting in multiple schools of thought.

Practicing Muslims rely on books and texts that systematize this knowledge and provide it in a practical form for daily use rather than go to the source material (which can be overwhelming if one wants to find, for example, the ruling on whether a certain action in a specific context is permissible or not). Most Muslim children, as part of their basic religious education, learn the basics of Islamic law and practice from such a book. That's usually enough to go through ones life.

The ruling on representational art is based on this kind of derivation. There are some exceptions (e.g. for educational, security etc. purposes) but they're generally narrowly circumscribed.

Sunni tradition relies primarily on the Quran and 6 books of Hadith (of which the two you've mentioned are the main ones). Shia tradition has a smaller Hadith corpus because of theological differences about the reliability of the chains of narration of the Hadith and hence the derived rulings are very different in some areas. I've generally seen Shia works of art where prophetic companions, angels etc. are pictured but non-realistically (unlike Christian iconography). Some of them blank out the faces but it's not a tradition I'm deeply familiar with so I don't know.

My theory is that the huge emphasis on calligraphy and tesselations in Islamic art is mainly because of this. We don't have (many) paintings and sculptures of religious figures like in the Christian traditions.

Only the Quran is guaranteed to be unchanged (but the interpretations and translations are not so guaranteed), the Hadiths are not.

The proper perspective is that if the Hadith and Quran are in conflict, the Quran is the authoratative source.

From our Sufi perspective, the Hadiths are a lot of game of telephone.

And if the Quran is difficult to apply, remember that compassion is the entire purpose of all God's religions.

Shiites often depict their important religious figures and martyrs, but with the face replaced with a bright glow.

Like this: https://www.deviantart.com/shia-ali/art/YA-ALI-343625919

It's also not uncommon to depict e.g. Ali with a face. Sunni salafist movements are the ones that are fanatically against such art, and they are quite savvy with propaganda and backed by very powerful friends on the peninsula and elsewhere, such as the backers of the Gulf dictatorships in London and Washington.

It does and it doesn't.

AFAIK Shia doesn't specifically ban all images outright, but instead relies on context. For example, the Prophet Muhammad (PBUH)* - Sunni Islam bans all images of him and other prophets, while Shia Islam might allow some images as a reference to him or other prophets as historical figures such as Jesus, Adam, Moses, David, etc... which they undoubtedly are. That's why some images of prophets are basically a white outline surrounded by fire, or a figure with a veil over their face. As long as you aren't defaming or purposely offending the religion, it's frowned upon in most cases, but not explicitly banned due to the historical context - humanity, after all, did and does rely on images instead of words at times and did so when most people were illiterate but could understand images. As long as the prophets aren't made into idols or worshiped or defamed, and are illustrated for historic context in a non defaming way, it's OK, sometimes.

*I say this while not Muslim to avoid the notion that I am purposely offending Islam - I'm not.