can a sorcerer (or other class with limited spells known) use a higher level spell slot to learn a lower level spell?
for example, bob the 11th level sorcerer has learned the four 3rd level spells he's allowed, but wants to learn fireball, too. can he learn fireball as a 4th level spell?
if so, is the spell treated as 3rd or 4th level for the purposes of saving throws, etc.?
can a sorcerer (or other class with limited spells known) use a higher level spell slot to learn a lower level spell?
for example, bob the 11th level sorcerer has learned the four 3rd level spells he's allowed, but wants to learn fireball, too. can he learn fireball as a 4th level spell?
if so, is the spell treated as 3rd or 4th level for the purposes of saving throws, etc.?
From what I can find, he simply can not learn fireball. The numbers on the sorcerers spells known list are absolute - you can't exchange a higher level spell known for a lower level one.
The sorcerer class and the magic chapter make no mention of a sorcerer being able to chose a lower level spell, and the sorcerer's spell swap ability specifically prohibits it.
Upon reaching 4th level, and at every even-numbered sorcerer level after that (6th, 8th, and so on), a sorcerer can choose to learn a new spell in place of one she already knows. In effect, the sorcerer loses the old spell in exchange for the new one. The new spell's level must be the same as that of the spell being exchanged. A sorcerer may swap only a single spell at any given level, and must choose whether or not to swap the spell at the same time that she gains new spells known for the level.
He could use a page of spell knowledge to get access to fireball, however.
i would just allow it by means of calling it a unique spell, although to be fair you might as well allow them to upgrade it somewhat to match what a 4th level spell could do... POSSIBLY to simplify things i would just allow you to "roll in" a 1 level metamagic effect, without needing the feat at all, nor needing casting time adjustment, and benefiting from higher spell level for DC... you are just limited by ALWAYS needing 4th level slot. i might not allow every metamagic if the result didn't match similar 4th level spells, but the point is just to allow something that is reasonable for a 4th level spell. at minimum, i don't see a problem with a unique spell duplicating fireball except being 4th level with a higher DC, that would be weaker than other 4th level spells. (strangely, by technically being a different spell things like spell immunity/contingencies vs. "fireball" would not work against it)
RAW doesn't cover that explicitly, although unique spells aren't specifically excluded by RAW either. designing spells is just a "meta" activity outside of scope of game rules. not really any different than picking up a new spell from a new source whether from Paizo or 3rd party.