Praise be to Allah.
Reading later parts of the Quraan before earlier parts is called Tankees (inversion). There are different types of Tankees:
Tankees al-Huroof (inversion of letters)
Tankees al-Kalimaat (inversion of words)
Tankees al-Aayat (inversion of verses)
Tankees al-Suwar (inversion of Soorahs)
Tankees al-Huroof (inversion of letters) means putting a later letter before a previous letter in one word, for example, instead of Rabb one reads Barr
Undoubtedly this is haraam, and invalidates a person's prayer, because it changes the Quraan from the way in which it was spoken by Allaah, and usually alters the meaning in a drastic manner.
(Al-Sharh al-Mumti by Ibn Uthaymeen, 3/110)
Tankees al-Kalimaat (inversion of words) means putting a later word before a previous word, for example, instead of Qul huwa Allaahu ahad, one reads Ahad Allaah huwa qul!
This also is undoubtedly haraam, because it changes the Quraan from the way in which it was spoken by Allaah.
(Al-Sharh al-Mumti, 3/110)
Tankees al-Aayat (inversion of verses) means reciting a later aayah before a previous aayah, for example, reciting min sharr il-waswaas il-khannaas before ilaah il-naas!
Concerning this, al-Qaadi Ayyaad (may Allaah have mercy on him) said:
There is no dispute concerning the order of the aayahs in each soorah. This is something which is Tawqeefi, i.e., based on revelation [and is not open to ijtihaad], and the order is that which now appears in the Mus-haf, and this is how the ummah transmitted it from the Prophet (peace and blessings of Allaah be upon him).
(Sharh al-Nawawi, 6/62. This was also the view of Ibn al-Arabi, as stated in al-Fath, 2/257).
Shaykh Ibn Uthaymeen said:
Tankees al-aayaat (inverting verses) is also haraam according to the most correct view, because the order of the aayahs is tawqeefi (something which is based on revelation [and not open to ijtihaad]). The meaning of tawqeefi is that it was dictated by the order of the Messenger (peace and blessings of Allaah be upon him).
(al-Sharh al-Mumti, 3/110).
Tankees al-Suwar (inversion of Soorahs) means, reciting later soorahs before earlier ones, for example, reciting Aal Imraan before al-Baqarah.
The ruling on this:
Those scholars who say that the order of soorahs is not tawqeefi do not see anything wrong with this.
Those who think that it is tawqeefi or that the consensus of the Sahaabah on the order of soorahs is evidence, do not think that it is permissible.
The correct view:
Is that the order of soorahs is not tawqeefi; it is the result of ijtihaad on the part of some of the Sahaabah.
There was no ijmaa (consensus) among the Sahaabah on the order of soorahs; the order in the Mus-haf of Abd-Allaah ibn Masood for example is different from that in the Mushafs of others.
In the Sunnah there is evidence that supports the view that it is permissible:
(A) Hudhayfah said: I prayed with the Prophet (peace and blessings of Allaah be upon him) one night, and he started to recite al-Baqarah. I thought, he will do rukoo when he reaches one hundred aayaat, but he kept going. I thought, he will complete it in one rakah, but he kept going. I thought, he will do rukoo now, but he started to recite al-Nisaa, and he recited all of it, then he started to recite Aal Imraan and recited all of it(Narrated by Muslim, 772).
The evidence in this hadeeth is that he recited al-Nisaa then Aal Imraan.
Al-Qaadi Ayyaad said: this contains evidence for those who say that the order of soorahs is the result of ijtihaad on the part of the Muslims when they wrote down the Mus-haf. The Prophet (peace and blessings of Allaah be upon him) did not dictate the order of soorahs; he entrusted this task to his ummah after his death. This is the view of Maalik and the majority of the scholars, and was the view favoured by al-Qaadi Abu Bakr al-Baaqillaani. Ibn al-Baaqillaani said: it is the more correct of the two views, although both are possible.
He said: what we say is that the order of soorahs is not binding when writing, praying, studying, teaching or learning. There is no report from the Prophet (peace and blessings of Allaah be upon him) concerning that which would make it forbidden to differ from it. Hence the order of soorahs in the various Mus-hafs differed, before the Mus-haf of Uthmaan.
The Prophet (peace and blessings of Allaah be upon him) and the ummah after him in all ages regarded it as permissible to differ from the order of soorahs in prayer, and when studying and teaching.
He said: with regard to the view of those scholars who say that (the order of soorahs) was set by the Prophet (peace and blessings of Allaah be upon him) and that he put them in the same order as appears in the Mus-haf of Uthmaan and that the different orders came about before they heard of his ruling and his final review of the Quraan with Jibreel they interpret the fact that he (peace and blessings of Allaah be upon him) recited al-Nisaa first and then Aal Imraan as meaning that this happened before the final ruling was dictated, and these two soorahs appear in this order in the Mus-haf of Ubayy.
He said: there is no dispute concerning the fact that a person who is praying may recite in the second rakah a soorah which comes before the soorah which he recited in the first rakah; but it is makrooh to do this in one rakah, or when reciting Quraan outside of salaah.
He said: but some of them permitted this.
The prohibition of the Salaf against reading the Quraan backwards is interpreted as referring to those who read from the end of a soorah to the beginning.
He said: there is no dispute concerning the fact that the order of aayaat in each soorah is based on revelation from Allaah and is as it now appears in the Mus-haf and as it was transmitted by the ummah from the Prophet (peace and blessings of Allaah be upon him).
(End of the comments of al-Qaadi Ayyaad). And Allaah knows best.
(Sharh Muslim, 6/61, 62).
The phrase [in the hadeeth of Hudhayfah] then he started to recite Aal Imraan means that it is not obligatory to follow the order of soorahs when reciting.
(Sharh al-Nisaai, 3/226).
(B) It was reported from Anas ibn Maalik (may Allaah be pleased with him) that a man from among the Ansaar used to lead them in prayer in the mosque of Qubaa. Every time he led them in prayer, he would start his recitation with Qul huwa Allaahu ahad, then when he finished it, he would recite another soorah. He did that in every rakah. His companions spoke with him and said, You always start with this soorah, then you do not think it is enough and you recite another. Either you should recite this soorah alone, or you should leave it and recite another. He said, I am not going to stop reciting it. If you like, I will lead you in prayer as I have been doing, and if you do not like it, I will leave you. They felt that he was one of the best of them, and they did not want anyone else to lead them in prayer. When the Prophet (peace and blessings of Allaah be upon him) came to them, they told him about this. He said, O So and so, what is stopping you from doing what your companions tell you? What makes you keep on reciting this soorah in every rakah? He said, I love it. He said, Your love for it will grant you admittance to Paradise.(Narrated by al-Bukhaari muallaqan, and by al-Tirmidhi with an isnaad similar to that of al-Bukhaari, 2901).
The evidence in this report is the fact that the man recited Soorat al-Ikhlaas in his prayer before any other soorah that comes before it (in the Mus-haf), and the Prophet (peace and blessings of Allaah be upon him) approved of that.
(C) This is the action of Umar (may Allaah be pleased with him).
Al-Imaam al-Bukhaari said:
Al-Ahnaf recited al-Kahf in the first rakah and Yoosuf or Yoonus in the second, and he said that he had prayed Fajr with Umar and he had done the same.
(Baab al-Jam bayna Sooratayn fil-Rakah, in Kitaab al-Adhaan).
With regard to the latter part of your question, we say:
It is permissible to recite aayahs 50-60 of al-Baqarah in the first rakah, then to recite aayahs 1-20 of al-Baqarah in the second rakah, because then the meaning of the passage will be complete.
But reciting aayahs 10-20 means that one is cutting off the meaning, so it is better not to do this. Perhaps you mentioned the numbers only by way of example and you did not mean these particular aayaat. And Allaah knows best.