For example on the 2nd rakkah of Fajr, is it satisfactory to ONLY recite surah Al Fatiha? Or is it farz to read an additional surah from the Quran after that?
It is satisfactory to recite only Surah Al-Fatiha in any rak'ah of any prayer. To read additional surah after 1st/2nd rak'ah is encouraged.
"'Ata' reported it on the authority of Abu Huraira who said: Recitation (of Surat al-Fatiha) in every (rak'ah) of prayer in essential. (The recitation) that we listened to from the Messenger of Allah we made you listen to it. And that which he recited inwardly to us, we recited it inwardly for you. And he who recites Umm al-Qur'an, it is enough for him (to complete the prayer), and he who adds to it (recites some other verses of the Holy Qur'an along with Surat al-Fatiha), it is preferable for him."- Sahih Muslim
You can read the text in Arabic here; search for Book 4, Hadith 46 https://sunnah.com/muslim/4
It is compulsory to recite in Fajr prayer any surah after surah Al Fatiha. The hadeeth in Bukhari, Muslim, Abu Dawood, Nasai and Ibn Majah, which states that the prophet (Allahs peace and blessings be upon him) use to read the fatihah followed by a surah in the first two rak’as.