One is not allowed to abandon reciting surah at-tawhid after having begun reciting it in salat. Is bismillah considered part of the surah and if one reads bismillah intending to recite surah at-tawhid, is he allowed to change his mind and recite another surah

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Bismillah is indeed independent part of the Quran. One is not allowed to recite Surah in salat without Bismillah. Doing so will renders the recitation incomplete.

Yes you are allowed to change your mind to recite different Surah

Yes you cannot abandon it unless if you are stuck and you don’t know what to do. In that case, you are allowed to recite new chapter with new Bismillah