Subhan Allah. Ustaz Rahmat started the lesson by highlighting that if one reflects on Surah al-Fateha and Surah An-Nas, it indeed come full circle - the importance of being consistent in one's tauhid to avoid shirk.
Ustaz continued from the previous lesson on "Basmalah", all the ulama agreed that it is part of the Quran. Read this for opinions if "Basmalah" is part of surah al-Fatihah. [Source: Tafseer ibn Kathir]
Nonetheless, in the case of solat, Ustaz Rahmat reinforced that it is wajib (obligatory) to recite the "Basmalah" in one's solat whether individually or in a jemaah (congregation) - jahar (loud and clear) or sir (for one's hearing only). Read this for the detailed explanation. [Source: Tafseer ibn Kathir]
Also, allow me to share the first part of a series of 5 lectures on Tafseer Bismillah:
[Source courtesy of SacredLearning.org]
From the perspective of Aqidah, a muslim is constantly in need of Allah's barakah (blessings) and when one does ibadah, with the sincere intent that it is for the love of Allah Azza wa Jalla, he will be rewarded (so constantly have the right intent in all that one does and begin with "Basmalah"). As part of adab, it is incomplete to say "Bismillah" (In the name of Allah). Instead, recite "Bismillahi Rahmani Rahim" (In the name of Allah, the Most Gracious, Most Merciful).
With the recital of the "Basmalah", one is to leave arrogance and cultivate humility, which is rightly so, as he is preparing to 'face' and submit to Allah SWT, his Creator. Ustaz pointed out that "Allah" is used because it is the exclusive name for Islam's rabb, in it entails the many beautiful and magnificent attributes of the Creator, subhan Allah.
I benefited tremendously from this article on "Bismillah & Its Blessings" and urge you to have a read. It may be 30-page long but its clarity in explanation will strengthen your conviction and create a mindfulness in your mind's eyes to always start your amal ibadah with "Basmalah", insya Allah.
Afternote: Indeed Islam is a simple and straightforward religion. Truly seeking Allah's barakah (blessings), forgiveness, safeguarding one from angels of Jahannam, etc, is so easy, if only we knew, subhan Allah! :)