For example, the spell 'Shift Blackwater' costs 10 pips and is a Star School spell. Well the maximum number of pips you can have is 7, 14 if it's your own school, but seeing as there are no Star Mastery Amulets, how is it possible to cast a 10 pip star school spell?
Shift Blackwater is a May Cast spell, which means you do not cast it yourself, but it is randomly cast when using a spell given by the same item. The pip value is for spells and cheats that take them into account for their effects.
For example, the spell 'Shift Blackwater' costs 10 pips and is a Star School spell. Well the maximum number of pips you can have is 7, 14 if it's your own school, but seeing as there are no Star Mastery Amulets, how is it possible to cast a 10 pip star school spell?
Magic, duh!
That spell and the ones like it are kind of "cheats" and are limited to items only. It's through the ability of your staff or whatever you're getting it off of. Your staff would be considered a "Item of Power" similar to a Sorcerer's Stone, Goblet of Fire, One Ring, etc. It does not draw off of your magical energy, but has it's own source of power as well.
From a technical perspective, it may be to discourage cheaters that try and exploit the game or it may be to just further illustrate the point that the item is special and not something that your wizard would regularly be able to do.
There are a few moon school spells that "shift" you briefly into another type of creature and you can do a one-time hit from a different school. I think those spells train in Khrysalis, around level 98. They will cost you pips. If you're shifting into a creature within your own school - or for which you carry a mastery amulet - you can use power pips and the cost is 3 pips. If you're shifting into an off-school creature, it will cost you double the pips. (So, for an off-school shift you'll pay 6 pips.)
Also, some wands have a "may-cast" ability that uses a creature with a different school (regular or astral) to do a significant amount of damage. You use the wand's regular hit and, occasionally, that will trigger a second and much bigger hit from the wand itself. These cost 0 pips to you.
If you're asking about the Myth school spell, I have not figured out how that darn thing works. It's insanely expensive, pip-wise, so I've only tried it a couple of times. For 6 pips, you trade "over-time" effects with someone on the opposing team. Trying to do this from second is not worth the effort and cost; it only sometimes has a benefit if you're going first. But in all honesty, a 4 pip Satyr makes more sense than spending 6 pips to somewhat reduce the effects of over-time spells.