I am having trouble with my troupe understanding exactly how casting requisites work. I know that they are treated as normal requisites for items, but I am interested in the details for spells.
Can you just use them in any formula you know?
Do you have to learn a formula with XYZ explicit casting requisites to be able to use them in casting?
As I understand it, if you know a formula like Leap of Homecoming, you can use any casting requisite on it, lowering the casting score of course, without having to learn any special version of it with casting requisites incorporated right? So it would be ReCo(Te) 35 for teleporting with a weapon, ReCo(Te/Vi) 35 for teleporting with a weapon and some vis etc...
I would let the magus teleport with just his clothes and talisman without any casting requisite at all, just so naked people appearing out of nowhere doesn't become silly. But for any more than simple clothes I would require a casting requisite. I feel like this is exactly the case as intended right? Am I missing anything?
You are pretty much correct. (Wait for it...someone will be along shortly to say neither of us are right...)
Whether a spell needs to have a form 'baked into' the design stage rather than just needing extra requisites when casting it can be a bit tricky, but generally adding casting requisites is easy whenever you need to affect an extra form of matter.
I usually designate teleport-type spells as either taking clothes/held items with the caster automatically (without using casting requisites but adding additional forms when creating the spell if they want to affect a full 'single size' bit of that form) or specifically teleport a naked body only (but requires casting requisites to keep your clothes). I don't allow the same spell to work either way. One is easier to cast; the other will get you out of manacles...
It's a YSMV issue, as far as I know. Some SG's will insist that you always have the requisites in the spell, others will allow you to design a spell to be varied on the fly. I prefer the on the fly approach since otherwise it makes some spell ideas useless and destroys the mythic'ness of the setting as a result...
Some spells, such as Unseen Porter, absolutely rely on it - without free casting req's the spell is a mere shadow of what it is intended to do.
This is the guidelines I use. These are my guidelines, and should not be treated as canon or official: they're just my interpretation:
Free requisites - Teleporting yourself and your clothes
Using unseen porter to levitate an object made of clay and wood.
The spell isn't changing from its base description, and the requisite simply means the spell works as intended in a non-silly way. The spell doesn't need to be designed with the requisite, but the requisite is calculated for casting totals.
Fundamental requisites - Shape of the Woodland Prowler
The spell literally can't function without the requisite, but the requisite is intrinsic to the spell design. In this case the requisite does count for both lab total and casting total, but the spell level isn't increased due to the requisite's presence.
I'm-trying-to-be-clever requisites - Transform air into poisonous gas and direct it - Mu(Re)Au
The requisite is adding additional functionality onto the spell that isn't needed for the base effect. In this case the requisite applies to both lab and casting total, and also adds to the level of the spell for complexity.