All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
The Prophetic narration about the excellence of the prayer in Al-Haraam mosque [Makkah] which states that it is better than 100,000 prayers in other mosques is authentic and it is reported by Ahmad, Ibn Maajah and others .
As regards the narration which reads “Friday is the Hajj of the poor.”, it is a weak narration and it is classified as such by some scholars among whom is Al-Albaani, Ash-Shawkaani and Al-Bayrooti .
With regard to your question that it is only the rich who get the reward of performing the prayer in Al-Haraam mosque, then the answer is that there is no doubt that Allaah favoured some places and some times over others, as Allaah Says (what means): {And your Lord creates what He wills and chooses.}[Quran 28:68]. The excellence of performing the prayer in Al-Haraam mosque is obtained by whoever performs the prayer in it, whether he is rich or poor. There are many rich people who did not perform the prayer in Al-Haraam mosque and did not visit it whereas there are many poor people who visited it and performed the prayer in it. What counts is to be blessed by Allaah to perform the prayer in it. There are also many people who perform the prayer in the above mosque while they are thinking about this worldly life whereby other people perform the prayer in very remote areas while being submissive and attentive, and there is a great difference in reward between the prayer of the first and the prayer of the second.
Anyway, whoever is unable to go to the Al-Haraam mosque, then Allaah facilitated for him many acts of worship that may surpass the reward of performing the prayer in Al-Haraam mosque. For instance, if a person performs the Fajr prayer and remains in his praying place mentioning Allaah until sunrise, and then he performs a two Rak'ah prayer, the reward of a full Hajj and 'Umrah will be written for him, as confirmed in a Prophetic narration.
Moreover, whoever wishes to go to Al-Haraam mosque if he had the money but is unable to go there because he does not have money, then he will get the reward of performing the prayer in it, Allaah willing. Indeed, the Prophet informed us about a man who says: “If I have the money as so and so, I will spend it in such and such (in charity)”, that ''they are equal in reward." [Ibn Maajah]
Finally, it should be noted that the questioner is well known to Islamweb as he asks so many questions, most of which are not of any practical benefit, so he should give the chance to others.