usually, 80%~100% are done by specialist "arranger", at least in the chinese market. there're also co-arranger like main arranger arranged everything and a special arrange just the strings part.

in western country, or even japan, they're done by the composer himself. producers also will do quite a lot as he/she'll involve lots of recording sessions and they'll put in lots of ideas there. heck, some producers are also the composer and also the arranger, which is quite common in japan.

then, sessionist and even mixing engineers can also input some ideas too, like guitarist replacing the midi guitar mockup, he can input some ideas too. sound engineers can copy some of the parts and paste it else where (maybe some special effects too).

how you give credits, it's entirely up to the whole team. but it's usually the one who did 80%~100%, or 50%/50% you'll see 2 names, or specifically like "arranged by xxx, strings by xxx".

wow, that means the specialist arranger must know very well for each instrument?
i mean he knows how to play each instrument? 
because he have to think back up vocal melody,
piano/guitar solo notes,
intro, outro and interlude how to play,
piano how to play,
guitar how to play,
string how to play,
bass how to play,
drum how to play...? 

local arranger usually don't deal with backing vocals, producers will hire backing vocal specialist, at least commonly done in the chinese market. but it's not uncommon for singers to DIY, or producers taking over the job.

and yes, arranger must know how all instruments are played, and more importantly, how to let them shine - you don't use classical guitar to play power chords, or piano to play like bass, etc etc. nowadays arranger all use MIDI to do arrangement, and most of the time, all of the tracks are MIDI because sampling technology nowadays are so good and computers are powerful enough to handle detailed and huge amount of samples. but it's up to the arranger (MIDI programmer) to make the midi track sound like real thing. still, nothing beats the real deal, but you know, it's about budget.

back then, almost everything are recorded with live players, and obviously sound so much more lively...

During the era of classical music, the arranger is the conductor, correct?

What type of skills must an arranger have? Knowledge of all instruments had alread been mentioned. Music theory is guess is a must. Anything else?