A few more questions
@occipitallobe :
So if we used a really subtle illusion and the mage didn't think to check they wouldn't know it's there?
Yes, but this is a lot rarer than you might think. Really subtle effects might work, but good practice involves casting detect magic (which is a fairly simple spell) every hour or so as standard, and anyone with a bit of cash will have a runed amulet, bracelet, or brooch that can be charged up and left to detect magic being cast around you for hours at a time. Of course, such an artifact only tells you if someone
is casting, whereas casting the spell yourself gives you more info, so you might be able to get away with an illusion in a magic-heavy environment.
Will experience in illusion magic carry over to some degree into other mental magic and does mental magic in general not require that much magic power?
Mental magic in general is tweaking things like the senses, memories, feelings, and so on. You can gain limited write-access to minds, but
not read-access. So if you're replacing someone's memories, you'd better have learned what actually happened in extreme detail first (for this reason most memory-replacement spells are temporary and have to be maintained, as the damage that can be done if you just start writing without having some idea of what to look for can be pretty bad). Most places won't teach you memory editing as it's seen as pretty horrifying, but if you're good enough you can hit your opponents with a wave of despair (or euphoria) powerful enough to prevent them from
wanting to cancel the spell.
Of course, if you miss just one of your opponents they can break your mental construct pretty easily, and they're very complex spells to cast, that can't be precast because they require on-the-fly editing based on the number of enemies, the sort of emotion you're trying to evoke, and your personal evaluation of their current emotional state (if you think they're angry, cast a despair spell, but they were actually joyful, you're liable to do nothing). You need to be
really good at casting spells to set one up in combat.
However, it is all very light on magic power.
Just how esoteric can alchemy get, like could we take someone who is particularly good looking and turn that into a potion or could we take some ones youth, also are any of these potions permanent?
In theory (as alchemical teachers will tell you), alchemy can do
anything. This is generally true for all magic, and a Grand Unifying Theory of Alchemy, Runes, Sigils and Spirits is something you'd be known for eternally if you could create one. As a rule, Runes are long-lasting, repeatable spells, Sigils are your standard spells, Spirits can do weird stuff but nobody really knows how they do it, and Alchemy transfers things - you generally need a base where the quality comes from, a magical substance to empower the transfer, a set of substances that synergise with the original substance to extract the desired quality (you could extract a cat's reflexes from a cat hair, a cat's sleepiness, or even a cat's proclivity to grow fur if you want to go full Harry Potter and prank someone), and a substance from the desired drinker (though this generally just means a human hair or nail clipping, most humans are similar enough that they can use potions made for any human, though if you use someone's hair or nail in
particular you'll get a better result).]
Making a potion's effects
permanent is impossible, though if you found a powerful enough source of magic you could make potions that lasted for two or three hundred years, which would have a similar effect.
edit: Potions that have effects on human bodies can be permanent in a sense. Take a potion that accelerated healing. You'd lose the healing factor after awhile, but you wouldn't get hurt again. Likewise, if you discovered a potion that reversed aging, you'd stop reverse aging after a bit, but you wouldn't re-age once the potion wore off. A cat fur potion, for instance, would make the fur grow on the body, but then the body would reject all the fur and it'd fall out shortly afterwards, returning to normal once the potion wore off.
In
practice, alchemy is extremely difficult, and about one-quarter to one-third of all potions you make will fail through no fault of your own - they just required specific conditions, and since modern equipment has frustratingly large margins of error in terms of measurement for heat, volume, etc, you'll have fallen prey to society's current level of technological advancement. A Extract of Youth is potentially possible, but nobody has ever succeeded at making one. You'll be able to do most things, but inventing a new potion might take three or four months of Actions outside class.
Alchemy has the same limitations as most spellcasting (mages are greedy and secretive about knowledge, and even at a magic school they'll disgorge
some of that hoarded knowledge, but usually only the mediocre stuff unless you can convince them you're trustworthy or it'll be worth their while), and generally speaking someone who gets really good at standard magic will have a
lot more options open to them than your standard Alchemist in most circumstances.