No, Allah ﷻ is not a tyrant.
This is just one of the many hadiths that I personally find really troubling... There are other hadiths which suggest, the polytheists' daughters who were buried alive in the reign of ignorance will also burn in hell.
The hadith you quoted from At-Tirmidhi is inaccurate, to say the least. Jami' at-Tirmidhi 117 is about a completely different topic, and I am unable to find any reference to it in the words you quoted, or similar words, apart from two hadiths about the children of the polytheists who die young: Sahih Muslim 2660 and Sahih Muslim 2661, in which the Prophet ﷺ did not say they were in hellfire; rather, that only Allah ﷻ knows what they would have done:
حَدَّثَنَا ابْنُ أَبِي عُمَرَ، حَدَّثَنَا سُفْيَانُ، عَنْ أَبِي الزِّنَادِ، عَنِ الأَعْرَجِ، عَنْ أَبِي هُرَيْرَةَ، قَالَ سُئِلَ رَسُولُ اللَّهِ صلى الله عليه وسلم عَنْ أَطْفَالِ الْمُشْرِكِينَ مَنْ يَمُوتُ مِنْهُمْ صَغِيرًا فَقَالَ " اللَّهُ أَعْلَمُ بِمَا كَانُوا عَامِلِينَ "
Abu Huraira reported that Allah's Messenger (way peace be upon him) was asked about the children of the polytheists who die young. Thereupon Allah's Apostle (ﷺ) said: It is Allah Who knows what they would be doing.
— Sahih Muslim 2660
These hadiths were also documented in Sahih al-Bukhari 1383, Sahih al-Bukhari 6597, Sunan an-Nasa'i 1949, Sunan an-Nasa'i 1950, Sunan an-Nasa'i 1951, and Sunan Abi Dawud 4711.
The children of Muslims go to Jannah as was narrated in this hadith (abridged):
صِغَارُهُمْ دَعَامِيصُ الْجَنَّةِ يَتَلَقَّى أَحَدُهُمْ أَبَاهُ - أَوْ قَالَ أَبَوَيْهِ - فَيَأْخُذُ بِثَوْبِهِ - أَوْ قَالَ بِيَدِهِ - كَمَا آخُذُ أَنَا بِصَنِفَةِ ثَوْبِكَ هَذَا فَلاَ يَتَنَاهَى - أَوْ قَالَ فَلاَ يَنْتَهِي - حَتَّى يُدْخِلَهُ اللَّهُ وَأَبَاهُ الْجَنَّةَ
Abu Hassan reported: I said to Abu Huraira that my two children had died. Would you narrate to me anything from Allah's Messenger (ﷺ) a hadith which would soothe our hearts in our bereavements? He said: Yes. Small children are the fowls of Paradise. If one of them meets his father (or he said his parents) he would take hold of his cloth, or he said with his hand as I take hold of the hem of your cloth (with my hand). And he (the child) would not take off (his hand) from it until Allah causes his father to enter Paradise. This hadith has been narrated on the authority of Tamim with the same chain of transmitters. And he is reported to have said: Did you hear from Allah's Messenger (ﷺ) anything which may soothe our heart in our bereavements? He said: Yes.
— Sahih Muslim 2635
To address the other categories in your question, this hadith in Majma' al-Zawāid (Arabic: مجمع الزاوئد ومنبع الفوائد) that has an authentic chain through Al-Bazzār:
عن أنس بن مالك قال : قال رسول الله - صلى الله عليه وسلم : " يؤتى بأربعة يوم القيامة : بالمولود ، وبالمعتوه ، وبمن مات في الفترة ، وبالشيخ الفاني ، كلهم يتكلم بحجته ، فيقول الرب - تبارك وتعالى - لعنق من النار : ابرز فيقول لهم : إني كنت أبعث إلى عبادي رسلا من أنفسهم ، وإني رسول نفسي إليكم ، ادخلوا هذه ، فيقول من كتب عليه الشقاء : يا رب أين ندخلها ومنها كنا نفر ؟ " قال : " ومن كتب عليه السعادة يمضي فيقتحم فيها مسرعا " قال : " فيقول الله - تبارك وتعالى : أنتم لرسلي أشد تكذيبا ومعصية ، فيدخل هؤلاء الجنة وهؤلاء النار " .
— NOTE: My own translation, so treat with care:
Narrated by Anas ibn Malik that the Prophet ﷺ said: "On the Day of Resurrection, four will be called upon: the newly-born, the mentally-challenged, those who were born in a fatrah (in between messengers), and perished old men, each bringing forth their argument. Allah ﷻ orders a portion of hellfire to appear, then Allah ﷻ tells this group:
I sent My messengers to My servants from amongst themselves. I am now My messenger to you. Enter this [the portion of hellfire].
Those who are doomed will say: 'How can we enter into which we were avoiding?'
Those who are saved will obey and willingly rush into it [the portion of hellfire].
Allah ﷻ then says to the doomed:
You would have been in more denial and disobedience to My messengers.
The doomed then enter the hellfire, and the saved go to Jannah.
Ths hadith addresses those who were not made aware of their duty to worship Allah ﷻ in their lifetime. They are tested instead on Judgment Day, then pass or fail in a similar fashion.
You can refer to the Gloss of Ibn al-Qayyim on Sunnan Abi Dawūd for more information (Arabic only).
Even the prophet's father I-e Abdullah seems to burn in hell. I think its very cruel not to allow people to be given a chance to choose right from wrong and then condemn them to hell for being polytheists.
The hadith of Anas ibn Malik in Sahih Muslim 203 (and other books) about the fathers of the Prophet ﷺ and the other man being in hellfire is indeed authentic, but it does not provide the reasons or the means by which they will end up in hellfire. As both being people of fatrah, they would be tested as per the hadith of Al-Bazzār above.
By these accords, people in hell will outnumber those in paradise by a huge proportion, simply because they were unlucky to be born to non believers and not able to grow old to change their faith.
It is not clear how you concluded that people in hell will outnumber those in paradise based on your quotations. Having said that, those who were born non-believers and were not given the chance to pursue a faith of their own choice will be tested as per the hadith of Al-Bazzār above.
There are other hadiths which suggests, the polytheists' daughters who were buried alive in the reign of ignorance will also burn in hell.
You did not mention which hadith(s) you are referring to, but I presume you are referring to the hadith by Salama Ibn Qays al-Ashja'i, which is not authentic. The several authentic hadiths about the children of the polytheists (referenced above) show otherwise.
Even though Mohammad pbuh himself was a polytheist at first and became a monotheist later exclusively because of the intervention made into his life by God.
There is no account in any book that the Prophet ﷺ was a polytheist. Such an allegation requires proof. The only verse that refers to anything close to this subject is about the Prophet ﷺ being guided by Allah ﷻ after being lost, i.e., had n o guidance. This does not translate into being a polytheist.
Furthermore, guidance is given to all of us in the form of the message of Allah ﷻ to us through His books and the teachings of His messengers and prophets. This is the "intervention" that we all receive, but some choose to embrace and some choose otherwise. In any case, punishment is only when the message is delivered:
مَّنِ اهْتَدَىٰ فَإِنَّمَا يَهْتَدِي لِنَفْسِهِ ۖ وَمَن ضَلَّ فَإِنَّمَا يَضِلُّ عَلَيْهَا ۚ وَلَا تَزِرُ وَازِرَةٌ وِزْرَ أُخْرَىٰ ۗ وَمَا كُنَّا مُعَذِّبِينَ حَتَّىٰ نَبْعَثَ رَسُولًا
Whoever is guided is only guided for [the benefit of] his soul. And whoever errs only errs against it. And no bearer of burdens will bear the burden of another. And never would We punish until We sent a messenger.
— Surat Al-Isra 17:15
Those who were not sent a messenger will be tested as per the hadith of Al-Bazzār above. In Tafsir Ibn Kathir of this verse, he mentioned that there is an agreement that the children of the Muslims go to paradise, quoting also Abu Ya'lā and Ahmad Ibn Hanbal. Ibn al-Qayyim mentioned the same in his gloss on Sunnan Abi Dawūd (referenced above), as did Al-Nawawi in Sahih Muslim bi Sharh al-Nawawi, and many others.
I personally find these hadiths very repulsive and cruel but may be I am wrong and the Quran might have a better more logical explanation to prove me wrong.
Reverting to the Qur'an only and ruling out authenticated hadiths is denying what is known of Islam by necessity. Having said that, the Qur'an does address your question in many verses:
ذَٰلِكَ بِمَا قَدَّمَتْ أَيْدِيكُمْ وَأَنَّ اللَّهَ لَيْسَ بِظَلَّامٍ لِّلْعَبِيدِ
That is for what your hands have put forth and because Allah is not ever unjust to [His] servants."
— Surat Āl-'Imrān 3:182
The same exact message is conveyed in Surat Al-Anfal 8:51, Surat Al-Haj 22:10, Surat Fussilat 41:46, Surat Qaf 50:29, among many others.