One of my players wants to put a staff of fire's effects on his already magical sword, it seems a little extreme, need to get some advice, is it even legal?
That would be a special item, and since weapons don't normally cast spells it would require GM approval. In short no.
Staves are for casting, not weapons. Not only that unless he can cast spells he could not use the staff properties anyway.
You could just hit somebody with the staff- since it isn't one of the kind of staves used for fighting I guess you'd treat it as an improvised weapon, but you can take Catch Off Guard to remedy that.
One of my players wants to put a staff of fire's effects on his already magical sword, it seems a little extreme, need to get some advice, is it even legal?
Why not.
So would this be a sword that can be recharged like a staff, hold 10 charges like a staff, but can deal non-blunt damage in melee?
Well, basic staff of fire is 19K (round up by 100 gp).
But he has to be a caster or UMD to use this thing (since its effects are staff mechanics). And it will be on a sword (not proficient unless Elf or Magus).
So I'd charged 3/4th price but again double that since not correct slot.
So flat price of 30K he can buy the addition to sword (no enhancement boost, it is a flat cost).
Or find an ally to craft it to sword for 15K.
Sure you could do this. Just multiply the cost of the cheaper item (the staff or the sword) by 1.5 and you will end up with a magic sword that also functions as a magic staff. I've done this in my games with magical spears.
Also, since it's a custom item, said player will need GM permission. If that's you, than all the better.
Depends entirely on what you think is "legal".
Staffs/weapons: staffs, in fact, are weapons: they're quarterstaves (and several call themselves out as magically enhanced quarterstaves in their description - i.e. those with a +1/+2/+3/etc bonus). Thus there is precedent for having magical weapons behaving like staffs, or vice-versa. (?).
As far as "official"... no, they're not (and thus probably not acceptable in Pathfinder Society modules - at least when played at conventions). At least, not explicitly. If you look in the back of the Core rule book, there are guidelines that allow "non-standard" (that is, not premade and printed in the book) magical items to be crafted by players and GMs and their rough estimates for pricing.
It is strongly suggested that you walk such a line with a careful hand, however, because it could easily be overpowered. That said, being a sword and having the powers of a staff of fire... not really overwhelming, and I wouldn't think it's overpowered at all. A more dangerous staff (like a staff of power!) would be far more worrisome.