Is the prayer valid if one only recites part of Surah Al-Fatihah, and only recites Surah Al-Ikhlas after the Takbirat Al-Ihram, and only says "Subhana Rabbiyal-A'la" twice in Rukoo' and Sujood, and contents oneself with this to catch the Imam, despite knowing the Hadiths and verses that encourage humility and perfecting the prayer?

The worshiper (ma'mum) must recite Surat al-Fatiha even if the Imam bows, and must complete it before following him. Tranquility (طمأنينة) is a pillar of prayer without which the prayer is invalid. This is supported by the Hadith of the one who prayed badly (al-Musi' Salatahu). If you are able to recite al-Fatiha with tranquility in the pillars, then your prayer is valid. As for devotion (khushu'), it is recommended, and the prayer is not invalidated by its absence.