android not detecting internal storage free space correctly

hay people,

so, today my friend gaved me his phone and asked me to install him facebook application on the phone, because he faild to install it.
so, i thought what an easy task, but it turns out i can not make it work at all.
so, he has samsung galaxy s4 (model: GT-I9500).
he has sd card which is 16 gb large, and his phone has 16 gb of installed storage. (at least phone specifications say so).

i tried to install facebook but i got the error.

the problem is that it says that there is no enouff storage available, and google play fails to download application.

so i went to the settings and some wery odd numbers i found.

so, it turns out that storage section of settings shows that there are three different storages.
first one is sd card.
for sd card it shows that it has 16.53 gb capacity, and that 13.97 gb is free.
second one is internal storage:
it shows that internal storage has 16gb capacity, from whitch (believe it or not) 15.91 gb is free.
furtermore, what is also strange is that it shows that there is third storage called "phone storage", and it shows that this storage has capacity of only 17.84 mb, and that 17.75 mb is free. but mb not gb.:eek::eek:

what is even stranger, if i go to applications section of settings to see installed apps it shows that available space for apps is 170 mb from witch about 40mb is free.

i mean wtf, how is that possible?

phone has 16 gb of internal storage, and almost all is empty, there are no installed applications except for built in ones, and still it looks like it lacks free space.
it almost looks like it looks at this "phone storage" for available space to install.

what is that "phone storage" at all?
why is only 17mb large?

and how to make android detect that there is 15.93 gb of internal storage available?
instead android shows that low space icon in status bar and every 5 minuts displays popup saying "internal storage is full".

please help to solve this.
why those 15.93 gb are not available for applications?


also, phone has an option to choose where to install applications.
and no matter what i choose (sd card or internal storage) it says there is no enough storage available.


please help.
i really want to fix his phone, because if i do not, you know, he would think that i do not know how to install facebook app. :(

any help?
how to solve this?
is this normal?
is there any system reserved memory or something?
if this is normal, than can someone explain why, what is all that free memory used for?

for far as i concern, i am down with ideas only to reset phone. but, i am hoping there is some better solutions.
for anyone who reply, thanx!