Answer

The bismillah alrahman al-rahim verse is part of every surah, as we believe every surah has bismillah alrahman al-rahim which is part of that surah, except surah al-tawbah. In terms of praying most Maraje’ say that bismillah alrahman al-rahim is part of every surah for Sayed Sistani who says that in the second surah the bismillah alrahman al-rahim is not part. If I intended to read a certain surah in the second surah of the prayer and I started the bismillah alrahman al-rahim and then I read another surah. If I wanted to go and read the surah that I intended to I go and read it without reading the bismillah alrahman al-rahim because when I said it my intention was for that surah. However, if I wanted to read the surah that I accidentally read to continue with that I must repeat the bismillah alrahman al-rahim so that the bismillah alrahman al-rahim that I intended to read with that belongs to that particular surah. If said for Sajdatol Sahow anytime you have said something extra or you have missed something then you do Sajdatol Sahow.

Generally speaking this rules which we have just mentioned applies, however there are certain surahs that have special requirements that when you do the bismillah alrahman al-rahim for them  then you may not change your mind, unless you do not know how to pronounce them properly. These two chapters are Surah Al-Kafiroon and Surah Al-Tawhid. If he intended to read Surah Al-Tawhid and he said bismillah alrahman al-rahim in the second surah then he said Surah Al-Nas here he does not have the option to go back to Surah Al-Nas, he must go back and read Surah Al-Tawhid. Even also if he intended to read Surah Al-Tawhid and he started with Surah Al-Kafiroon he still must go back to Surah Al-Tawhid.