How is magic use regulated? If magic is outlawed, why? 

In mine it is. 

At some time in the past (before the start of the novel series this magic system is used in) too many mages went power crazy. Law had to step in. Rules, regulations, laws, and ordinances govern magic arts with a fine tooth comb. Now being a mage requires certification, permits, license, PhDs, building inspections, etc, similar to real world doctors before they can work at hospitals or real world restaurants. Becoming a mage as a career, setting up a magic shop, becoming a mage for hire, all require huge amounts of legal red tape and approval from bureaucrats who make Hitchhiker's Guide to the Galaxy Vogons look loosey-goosey.

Practicing magic without the correct and proper paperwork can land a mage with huge fines at minimum, in jail or prison in most cases, and in some cases result in life time solitary confinement in a special mental institute just for mages, where they keep the mages straightjacketed in special anti-magic fabric and shackled in a techo-faery-iron, most mages there are lobotomized and physically tortured with medical experiments as well. Nothing is more feared in the world, than this mental-institute-prison for mages, and the fear of it alone is enough to keep most from even thinking about learning magic.

Some forms of magic are allowed, things considered "good" or "holy" or "healing" are generally the least regulated. So you see mages in medical careers, hospitals run by healing mages, churches run by mage-priests who do laying-on-of-hands magic-healing, science-mages who create new advances in healing potions or techno mages who invent magical household items (flying cars, self-sweeping brooms, self-boiling teapots, etc), swamp witches who double as midwives and make herbal potions to heal sick livestock. That so of thing, is seen as respectable in the eyes of the law, and those types of magic careers are easiest to get approved and licenced for.

Other forms of magic are allowed on a limited basis with extreme levels of men-in-black style secret agent government scrutiny. For example, portal magic and time travel are allowed for a few, limited individuals who have gone through extreme levels of rigorous government testing, to prove they can be trusted. Changing history "the wrong way" is seen as a devastatingly evil crime, unless the government decides a certain event needs changing and hires the mage to change it. 

Most of the world has no idea that portals or time travel exist, only a few governments have access to the ability/tech, and guard it's secret lustfully. Thus a mage hired to be a part of the program, has his identity changed, and who he was before essentially ceases to exist, with him no longer allowed to live free in public society. No one chooses this life as it is near life imprisonment. All mages in the program were kidnapped and forced into it against their will and only stay in it because they are too scared not to be in it, after being shown footage of other mages being tortured to death for escaping.

And then there are forms of magic that are outright banned, with the practitioners seen as criminals and arrested, fined, imprisoned, or tortured if caught. Necromancy, divination by communicating with spirits, demonology, familiars, blood magic, resurrection of the dead, sex magic, death magic, Chaos magic, and other such things, will land a mage in the mental institute or even warrant execution.

And then there are the corrupted power hungry leaders who make the laws, and are known to abuse the laws to their favor. For example, it is common practice for many Justice Mages, to frame their competition, some mage with all his paperwork in order, not practicing outlawed magic, could suddenly find himself accused of Necromancy and sent to prison after conveniently planted human bones were found in a box in his closet, planted there by the Justice Mage doing the inspection.

  *   If magic items are outlawed, why? 

Many magic items are illegal. 

Gemstones naturally possess magic powers, resulting in most mages wear a lot of bling, because certain types of crystals enhance certain types of powers. 

Mages will often have a dozen or more piercings in each ear, lip piercings, nose rings, nipple rings, toe rings, any place they can add a ring with a crystal charm or gemstone in it, they will. Runes and animal shaped charms and sigil talismans are often hung on the rings, these adding more enchantments. 

The most powerful mages give Liberace a run for his money with the over the top gem encrusted robes and capes. Magic can be embedded into cloth via weaving patterns, embroidery, or beadwork as well. 

Every colour adds power to corresponding spells, so mages are prone to wear eye popping day glow colours: hot pinks, neon yellows, day glow orange, phosphorescent lime green. 

You KNOW a powerful mage when you see them, because they are covered in bling, bling, bling, and more bling on top of eye blinding colours. 

The has caused society as a whole to fear flashy jewelry, beading and embroidered clothing, bright coloured fashions, etc. These things are outlawed in most towns, and confiscated and burned or otherwise destroyed by the Justice Mages.

Most people wear shades of black, brown, navy blue, or grey, and any jewelry is simple bands of silver or gold without gems or stones or charms. The general public is scared of bright coloured clothe and flashy jewelry, because people caught wearing such things can be accused of being mages and killed by the Guild's Justice Mages.

Any magic item that is used to make mages more powerful is outlawed, while household magic items (the flying cars, self-sweeping brooms, self-boiling teapots, etc mentioned before ), are allowed, but regulated via permits and licences, the same way real world gun laws are.