Is the prayer of the Hanafis valid if one doubts the number of rak'ahs or which rak'ah one is in, and builds upon their predominant conjecture, or at least if they do not have a predominant conjecture, then performs the prostration of forgetfulness (sujud al-sahw) after the tasleem?

The Hanafi school of thought concerning one who doubts in their prayer:

If the doubt occurs for the first time, one should interrupt the prayer with an action that invalidates it, and then restart the prayer.

If the doubt recurs frequently (two or more times in one's lifetime or in a year), one should act upon their strongest presumption, if such exists, and perform the prostration of forgetfulness (sujud al-sahw). If no strong presumption exists, one should build upon the minimum (i.e., assume the lesser number) and perform the prostration of forgetfulness. According to them, the prostration of forgetfulness is always performed after the salutation (taslim).

This ruling is not exclusive to doubting the number of rak'ahs but also includes doubting the number of prostrations and other elements of the prayer.