Your question consists of two parts:
The status and fate of Jews and Christians
The orthodox creed is that the current Jews and Christians are disbelievers and will be in Hell in the hereafter. Accepting Judaism and Christianity to be the same as Islam or acknowledging the followers of these religions to be 'believers' - is considered heretical.
وأن من لم يكفر من دان بغير الإسلام كالنصارى، أو شك في تكفيرهم، أو صحح مذهبهم، فهو كافر
Whoever does not acknowledge the Kufr of religions other then Islam, such as the Christians, or doubts their disbelief or considers their religion to be correct - then he himself is a Kafir
— Rawdat al-Talibeen- Imam Nawawi
أو لم يكفر من دان أي تدين بغير الإسلام، كالنصارى واليهود أو شك في كفرهم، أو صحح مذهبهم فهو كافر
Whoever does not acknowledge the Kufr of religions other then Islam, such as the Christians or Jews, or doubts their disbelief or considers their religion to be correct - then he himself is a Kafir
— Kashshaaf al-Qinaa’ - Al-Bahooti
وقائل هذا كله كافر بالإجماع على كفر من لم يكفر أحدا من النصارى واليهود وكل من فارق دين المسلمين أو وقف في تكفيرهم أو شك
There is scholarly consensus on the fact that the one who does not regard any of the Jews and Christians ... as disbelievers, or who refrains or hesitates to describe them as disbelievers, is himself a disbeliever.
— Shifa - Qaadi ‘Iyaad
That is because of their false beliefs regarding Allah (e.g. Trinity) and their rejection of Muhammad ﷺ and the Quran. There are numerous verses where Allah has explicitly and implicitly called them disbelievers and differentiated between their religions and Islam, such as in : 2:91, 2:120, 2:135, 3:19, 3:67, 3:70, 3:98, 4:150-151, 4:155, 5:65, 5:68, 5:72, 5:73.
Them being in Hell is also stated within the Quran:
إن الذين كفروا من أهل الكتاب والمشركين في نار جهنم خالدين فيها أولئك هم شر البرية
Indeed, they who disbelieved among the People of the Scripture and the polytheists will be in the fire of Hell, abiding eternally therein. Those are the worst of creatures.
— Quran 98:6
And in Sahih ahadith:
لا يسمع بي أحد من هذه الأمة يهودي ولا نصراني ثم لم يؤمن بالذي أرسلت به إلا كان من أصحاب النار
Whoever amongst the community of Jews or Christians hears about me, but does not affirm his belief in that with which I have been sent and dies in this state, he shall be but one of the denizens of Hell-Fire.
— Sahih Muslim 153
كان غلام يهودي يخدم النبي صلى الله عليه وسلم فمرض، فأتاه النبي صلى الله عليه وسلم يعوده، فقعد عند رأسه فقال له " أسلم ". فنظر إلى أبيه وهو عنده فقال له أطع أبا القاسم صلى الله عليه وسلم. فأسلم، فخرج النبي صلى الله عليه وسلم وهو يقول الحمد لله الذي أنقذه من النار
A young Jewish boy used to serve the Prophet (ﷺ) and he became sick. So the Prophet (ﷺ) went to visit him. He sat near his head and asked him to embrace Islam. The boy looked at his father, who was sitting there; the latter told him to obey Abul-Qasim and the boy embraced Islam. The Prophet (ﷺ) came out saying: "Praises be to Allah Who saved the boy from the Hell-fire."
— Sahih Bukhari 1356
Also refer to: Do modern-day Jews, Sabians and Christians have "nothing to fear or to regret" (Qur'an 5:69)?
Levels of Hell
There are multiple gates / levels of Hell. This is evident from the following verse:
وإن جهنم لموعدهم أجمعين لها سبعة أبواب لكل باب منهم جزء مقسوم
And indeed, Hell is the promised place for them all. It has seven gates; for every gate is of them a portion designated.
— Quran 15:43-44
Similarly it is proven that some groups will be in the lowest level and receive the severest punishment:
إن المنافقين في الدرك الأسفل من النار
Indeed, the hypocrites will be in the lowest depths of the Fire
— Quran 4:145
ويوم تقوم الساعة أدخلوا آل فرعون أشد العذاب
And the Day the Hour appears [it will be said], "Make the people of Pharaoh enter the severest punishment."
— Quran 40:46
قال الله إني منزلها عليكم فمن يكفر بعد منكم فإني أعذبه عذابا لا أعذبه أحدا من العالمين
Allah said, "Indeed, I will sent it down to you, but whoever disbelieves afterwards from among you - then indeed will I punish him with a punishment by which I have not punished anyone among the worlds."
— Quran 5:115
Some have held that the levels are the same as gates, while some have held that the gates are independent of the levels.
The seven names
جهنم and لظى and حطمة and سعير and سقر and جحيم and هاوية are present in the Quran as names of Hell - however it is not evident that they are names of individual gates \ levels within hell as appears in some traditions.
What you have quoted regarding the seven levels of hell and its residents seems to be an adaptation of the traditions that have been narrated in the exegesis of verse 15:44.
قال ابن جريج : النار سبع دركات : أولها جهنم ، ثم لظى ، ثم الحطمة ، ثم السعير ، ثم سقر ، ثم الجحيم ، ثم الهاوية .
...
وقال الضحاك : في الدركة الأولى أهل التوحيد الذي أدخلوا النار ، يعذبون بقدر ذنوبهم ثم يخرجون ، وفي الثانية النصارى ، وفي الثالثة اليهود ، وفي الرابعة الصابئون ، وفي الخامسة المجوس ، وفي السادسة أهل الشرك ، وفي السابعة المنافقون
Ibn Jurayj said: Hell has seven levels: first one is Jahannam, then Lazaa, then Hatamah, then Sa’eer, then Saqar, then Jaheem and then Haawiyah ...
Dhahak ibn Muzahim said: The first level is for the people of tawheed (Muslims) who would enter the fire, they will be punished to the extent of their sins and then will be removed from hell. The second is for Christians, the third is for Jews, the fourth is for Sabeans, the fifth is for Zoroastrians, the sixth is for the Polytheists and the seventh is for the Hypocrites.
— Tafsir al-Baghawy also see Tafsir Ibn Abi Hatim and Tafsir al-Tabary
