Praise be to Allah.

We should understand properly the general principle concerning this matter, the matter of entering Paradise and spending eternity in Hell. It is a simple matter that is explained in a brief hadeeth that was narrated by Muslim in his Saheeh (135) from Jaabir (may Allah be pleased with him) who said: A man came to the Prophet (blessings and peace of Allah be upon him) and said: O Messenger of Allah, what are the two deeds that make entering Paradise or Hell inevitable?

He said: “Whoever dies not associating anything with Allah will enter Paradise, and whoever dies associating anything with Allah will enter Hell.” 

An-Nawawi said: With regard to the words, “What are the two deeds that make entering Paradise or Hell inevitable?” what is meant are the characteristic that makes Paradise inevitable and the characteristic that makes Hell inevitable. End quote. 

This hadeeth explains that what makes it inevitable that a person will enter Paradise is if he dies believing in Tawheed, and what makes it inevitable that a person will spend eternity in Hell is if he dies believing in shirk. 

This is a definitive principle that is well-known and well established in the religion of Islam. There are mutawaatir texts which confirm and affirm it. Allah, may He be exalted, 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 pleases, and whoever sets up partners with Allah in worship, he has indeed invented a tremendous sin”

[an-Nisa’ 4:48]. 

The Prophet (blessings and peace of Allah be upon him) explained, in the hadeeth about intercession, the situation of the sinners in Hell, and he explained that no one will be brought out of Hell except those who died believing in Tawheed and uttered the Shahaadah (testimony of faith), and had in their hearts something of faith: “There will be brought out of the Fire anyone who said, Laa ilaaha ill-Allah (there is no god but Allah) and had in his heart goodness equal to the weight of a grain of barley. Then there will be brought out of the Fire anyone who said Laa ilaaha ill-Allah (there is no god but Allah) and had in his heart goodness equal to the weight of a grain of wheat. Then there will be brought out of the Fire anyone who said Laa ilaaha ill-Allah (there is no god but Allah) and had in his heart goodness equal to the weight of a small ant.”

Narrated by al-Bukhaari, 6861; Muslim, 285. 

Based on that, we can find out the situation of those mentioned in the question. 

1.

If a person fell into major shirk, whether he was originally a mushrik like the Jews, Christians, Buddhists and other types of disbelievers, or he was a Muslim then he apostatised from Islam by falling into major shirk – as mentioned in the question – then his claim to belong to Islam or his having a Muslim name will be of no benefit to him, and neither will any good deeds that he did and so on, if he fell into major shirk and died in that state without having repented. Allah, may He be exalted, says (interpretation of the meaning):

“And indeed it has been revealed to you (O Muhammad SAW), as it was to those (Allahs Messengers) before you: ‘If you join others in worship with Allah, (then) surely (all) your deeds will be in vain, and you will certainly be among the losers.’

Nay! But worship Allah (Alone and none else), and be among the grateful”

[az-Zumar 39:65-66]. 

2.

The one who does not pray at all, either in his house or in the mosque, and does not attend Jumu‘ah or prayers in congregation, has also rendered his good deeds invalid and has falling into kufr by not praying at all. The Messenger of Allah (blessings and peace of Allah be upon him) said: “The covenant that stands between us and them – i.e., the characteristic that separates the Muslims from the disbelievers – is the prayer. Whoever does not pray has disbelieved.”

Narrated by at-Tirmidhi, 2545; an-Nasaa’i, 459. classed as saheeh by al-Albaani. 

For more information on the kufr of the one who does not pray, see the answer to question no. 5208 

3.

With regard to the hypocrites, if what is meant is the people of major hypocrisy, namely those who make a show of being believers in this world when they are concealing kufr in their hearts and hiding it from the people, they will be in a worse position than the kuffaar and mushrikeen. Hence their fate will be in the lowest levels of Hell, as Allah, may He be exalted, says (interpretation of the meaning):

“Verily, the hypocrites will be in the lowest depths (grade) of the Fire; no helper will you find for them”

[an-Nisa’ 4:145]. 

4.

But if what you meant by hypocrites is those who fall into some acts of hypocrisy, such as lying or betraying a trust or breaking a promise; or he fell into some kind of minor shirk, such as showing off or swearing by something other than Allah; or who fell into some major or minor sin – such a person does not become a kaafir just by doing that thing. It does not put him beyond the pale of Islam and he will not spend eternity in Hell because of it, if he dies believing in Tawheed. Rather his case is up to Allah: if He wills He will punish him for his sin, then admit him to Paradise because of his belief in Tawheed, or He will bestow His grace upon him from the outset and admit him into Paradise and forgive him for the sins that he committed. Al-Bukhaari (6933) and Muslim (1659) narrated that Abu Dharr said: The Messenger of Allah (blessings and peace of Allah be upon him) said: “Jibreel appeared to me at the side of the harrah and said: ‘Give your ummah the glad tidings that whoever dies not associating anything with Allah will enter Paradise.’ I said: ‘O Jibreel, even if he steals and even if commits zina?’ He said: ‘Yes.’ I said: ‘Even if he steals and even if commits zina?’ He said: ‘Yes.’ I said: ‘Even if he steals and even if he commits zina?’ He said: ‘Yes, and even if he drinks alcohol.’” 

And Allah knows best.