No, no, yes.
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yes, yes, no.
but you can have a wand of it.
note it has no target entry. so it cannot be cast on someone else.
the wording of the spell is always "you", as normal for a personal spell.
its implicitly personal.
Component: V, S
Range 60 ft.
Area cone-shaped emanation
Duration concentration, up to 1 min./level (D)
Saving Throw none; Spell Resistance no
a 60 ft. cone-shaped emanation coming from you.
no save for creatures in the area of the emanation, no sr applies to creatures in the emanation.
Detect magic has no target line; it has an area. That means it can't be cast on people, and therefore can't be made into a potion.
I would say no, no, no. But as has been pointed out above, it has the features of a personal spell without explicitly being called one, so I'm not positive on the first answer. Are there any rules interactions where this matters? I know it will for other detect spells if the devs decide to nerf the alchemist's ability to make infusions of personal extracts.
Just let him find an item that casts detect magic. I'm pretty sure one exists in the myriad of items for Pathfinder already.
Edit: Even better, let him add the trait Two World Magic and select Detect Magic as the spell. Technically he could take the feat that lets you add extra traits and pick it up that way, but I think letting him exchange a trait or giving him an item that casts it is easiest.
Just let him find an item that casts detect magic. I'm pretty sure one exists in the myriad of items for Pathfinder already.
The only one I know of is a special kind of Wayfinder, but it's for PFS and costs Prestige Points to get instead of cash.
Even better, he gets Arcane Sight cast on him permanently. Its even better than detect magic, only drawback is the possibility of being overwhelmed by magical auras.
Edit: Not even a thing, I was htining it was similar to Detect Evil et al. but there doesn't appear to be the same ling about overwhelming magic stunning you.
That spell can only be made permanent FOR THE CASTER.
Good point, didn't think it all the way through.
So, back to the item that casts detect magic. A use acitvated version on a slotless item would be 4000 gp I think.
Edit: If he had sufficient UMD score he could UMD a scroll of permanency then a scroll of arcane sight.
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Thanks everyone, I'm pretty sure myself that it can't be cast on someone else or made into a potion but the lack of 'Range: Personal' makes this up for debate.
It matters for a character with Spellcraft (to use Crafting feats, taken through a SLA) but lacks the spell and who wants to identify magic items.
Alchemists need to use either an infusion of Identify, or a wand of Detect Magic for items other than potions. I would almost recommend one or the other for your character, and UMD to activate the wand. It sucks but at least wands of detect magic are rather cheap. A wand of Identify can be pretty handy anyway, for the +10 to identify magic items.
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potions/oils have the same requirement. the spell must be able to target one or multiple creatures. so it can't have an area component. if it does, like haste, it'll say one or more creatures in a such and such area.
detect magic lacks that.
so no potions or oils, except in home games.
if you want to make something that violates this, its generally an Elixr or a wondrous item.
i'd go for goggles that let you detect magic a few times/day. many casters i know in home games go for custom gloves that provide a skill bonus to spellcraft, so they can make magic items faster, gloves that do that, and let you detect magic via contact while handling an item don't seem outrageous, and they're limited to what you can touch.