Meaning of Abiding for Eternity in Hell
Question

Allah says (interpretation of the meaning): “Verily, Allah forgives not that partners should be set up with Him (in worship), but He forgives except that (anything else) to whom He wills…” [al-Nisa 4:48] 
“And whoever kills a believer intentionally, his recompense is Hell to abide therein…” [al-Nisa 4:93] 
I hope that you could explain how to reconcile these two verses.
Praise be to Allah.Shaykh ‘Abd al-‘Aziz ibn Baz (may Allah have mercy on him) said: 
Meaning of abiding for eternity in Hell for committing shirk 
 “There is no contradiction between them – praise be to Allah. In the first verse, Allah is telling His slaves that any sin less than shirk (associating others in worship with Him) is subject to His will: He may forgive it by His grace, or He may punish the person who dies in sin in a way commensurate with his sin, because he transgressed the sacred limits of Allah and did that which deserves the wrath of Allah. But the mushrik (one who associates others with Allah) cannot be forgiven, rather he is doomed to Hell for eternity, to abide therein forever, if he dies in shirk – we seek refuge with Allah from that. 
Meaning of abiding for eternity in Hell for committing murder
With regard to the second verse, this is a warning to one who kills a person unlawfully, that he will be punished and that Allah is angry with him for that. Hence Allah says (interpretation of the meaning): 
“And whoever kills a believer intentionally, his recompense is Hell to abide therein; and the Wrath and the Curse of Allah are upon him, and a great punishment is prepared for him” [al-Nisa 4:93]
What this means is that this is the punishment if Allah punishes him, and he deserves that; if Allah forgives him then He is All-Forgiving. He may be punished with what Allah mentions of a period of time spent in Hell, then Allah will bring him forth from the Fire. This is a temporary abiding in Hell, which is not like the abiding of the unbelievers. For abiding for eternity in Hell is of two types, eternal abiding which never ends, which is the abiding of the unbelievers in Hell, as Allah says concerning them (interpretation of the meaning): 
“Thus Allah will show them their deeds as regrets for them. And they will never get out of the Fire.” [al-Baqarah 2:167]
And Allah says in Surah al-Maidah (interpretation of the meaning): 
“They will long to get out of the Fire, but never will they get out therefrom; and theirs will be a lasting torment.” [al-Maidah 5:37]
Destiny of sinners
With regard to sinners, such as the one who kills a person unlawfully, the one who commits adultery, the one who disobeys his parents, the one who consumes riba, the one who drinks alcohol and so on, if they die in their sin and they are Muslims, then they are subject to the will of Allah, as He says (interpretation of the meaning): 
“but He forgives except that (anything else) to whom He wills…” [al-Nisa 4:48]
So if He wills, He will forgive them because of the righteous deeds with which they died, such as their believing in Allah Alone (Tawheed), their sincerity towards Allah and their being Muslims, or because of the intercession of those who intercede for them, as well as their Tawheed and sincerity. 
Or He may punish them and not forgive them, so He will punish them by causing them to enter Hell and tormenting them therein, in a manner commensurate with their sin, then he will bring them forth therefrom, as is mentioned in many ahadith from the Messenger of Allah (peace and blessings of Allah be upon him), who said that he will intercede for the sinners among his ummah, and that Allah will set a limit for that several times, so he will intercede and bring forth a number of them by Allah’s leave, then he will intercede again and again and again; he (peace and blessings of Allah be upon him) will intercede four times. Similarly the angels, the believers and the children who died before reaching the age of adolescence and before their parents died, will all intercede and Allah will bring forth whomever He wills from the Fire because of their intercession. Then some sinners among those who believed in Tawheed and Islam will be left in Hell, and Allah will bring them forth by His grace and mercy without any intercession, then there will be no one left in Hell except those whom the Quran has ruled will abide therein forever, namely the kuffar. 
Thus the questioner will understand how to reconcile these two verses, and similar texts and the ahadith which promise Paradise to those who die in Islam, except those whom Allah wishes to punish for their sin. And He is the most Wise and most Just in that; He rules as He wills and does what He wants. 
And there are some whom Allah will not punish, by His grace, for many reasons, such as righteous deeds and because of the intercession of the intercessors, and above all that because of His Mercy and Grace. 
For  more, please see these answers: 169677 , 211871 , 45804 , and 200632 .
And Allah knows best.