To what extent is the Hajj valid for someone who stoned the Great 'Aqabah pillar, shaved, exited the state of ihram, stayed overnight in Mina on the 11th and 12th, stoned the jamarat, and then performed the farewell tawaf without performing the tawaf al-ifadah due to ignorance of it?

As long as you have not performed Tawaf Al-Ifadah, you remain in your state of ihram. You must now proceed to Mecca and perform Tawaf Al-Ifadah, and perform Sa'i between Safa and Marwah if you are a Mutamatti' or if you did not perform Sa'i with Tawaf Al-Qudum, for Sa'i is not valid except after a correct tawaf.

If you do that, your ritual will be complete. If you are unable to go to Mecca, you are considered "muhsar" (prevented) and can exit ihram by offering a sacrifice (hady). If this was Hajj Al-Islam, it remains an obligation upon you and is not waived; you must perform it when you are able. If it was not Hajj Al-Islam, you are not obligated to make it up.

If you are unable to offer the sacrifice, you can exit ihram by fasting ten days, by analogy with the Mutamatti' who cannot find a sacrifice. As for sexual intercourse before you knew the ruling, it is forgiven due to your ignorance of the Sharia's ruling. Allah Almighty said: "And there is no blame upon you for that in which you have erred, but [only for] what your hearts intended. And ever is Allah Forgiving and Merciful." (Al-Ahzab: 5).