Is it permissible to call upon a dead wali (“saint”) or Hazrat ‘Ali

First of all, we must comment on your saying in your question, “or any other being apart from Allah…” We must point out that this wording is wrong, because it may be taken as meaning that you think that Allah is a created being; but we are sure that you do not believe that.

Firstly:

Allah said to His Prophet (peace and blessings of Allah be upon him):

“Verily, you (O Muhammad) will die, and verily, they (too) will die” [al-Zumar 39:30]  

And Allah said (interpretation of the meaning): 

“Muhammad is no more than a Messenger, and indeed (many) Messengers have passed away before him. If he dies or is killed, will you then turn back on your heels (as disbelievers)?” [Aal ‘Imraan 3:144]

“And We granted not to any human being immortality before you (O Muhammad); then if you die, would they live forever? [al-Anbiyaa’ 21:34]  

Abu Bakr (may Allah be pleased with him) said, in his speech after the Prophet (peace and blessings of Allah be upon him) had died, “Whoever used to worship Muhammad, Muhammad has died, but whoever used to worship Allah, Allah is Alive and will never die.” (Narrated by al-Bukhaari).

This and similar evidence indicates that Muhammad (peace and blessings of Allah be upon him) was a human being like all other human beings, who died as they die, and will never be immortal just as no one before him was immortal.

Whoever wants to put the Prophet beyond the human realm and claim that the Prophet is present in all places, is the one who should be asked to produce evidence (daleel). How does he know that the Prophet is omnipresent at all times? Moreover, those who make the same claim with regard to Allah (should know that) this is kufr, deviation and misguidance. This belief implies that Allah is present even in dirty places like bathrooms etc. – Glorified be Allah far above what they say.

Secondly:

-You have to read the book Fath al-Majeed Sharh Kitaab al-Tawheed, by Shaykh ‘Abd al-Rahmaan ibn Hasan.

-Know that du’aa’ and asking for help are forms of worship, as Allah says (interpretation of the meaning):

“And your Lord said: ‘Invoke Me [i.e. believe in My Oneness (Islamic Monotheism) and ask Me for anything] I will respond to your (invocation). Verily, those who scorn My worship [i.e. do not invoke Me, and do not believe in My Oneness, (Islamic Monotheism)] they will surely enter Hell in humiliation!’” [Ghaafir 40:60]

And according to a report narrated by al-Tirmidhi, the Prophet (peace and blessings of Allah be upon him) said: “Du’aa’ is worship.”

 So it is not permissible to offer du’aa’ to or call upon anyone except Allah. But the evidence indicates that it is permissible to ask another person for some things, but that is subject to two conditions : 

1-That it should be something possible and the person should be able to do it, such as asking a person to give you money when you are in need of it. But if it is something that he is not able to do, then it is not permissible for you to ask him, such as asking a man to let you be one of the people of Paradise, because he is not able to do that even if he is a righteous and pious man.

2-The person who is asked should be capable, such as one who is alive. It is not permissible to call upon the dead, as Allah says (interpretation of the meaning):

“And those, whom you invoke or call upon instead of Him, own not even a Qitmeer (the thin membrane over the date stone).

If you invoke (or call upon) them, they hear not your call; and if (in case) they were to hear, they could not grant it (your request) to you [Faatir 35:13-14]