Is it permissible to change one's intention in a single act, such as someone who intended to pray a supererogatory prayer (nafilah) then remembered that he wanted to pray Istikhara? And what is the evidence for that? Is it permissible to combine two intentions in one act, such as the intention of Udhiyah and Aqiqah in a single sacrifice?

It is permissible to combine the intention of Tahiyyat al-Masjid (greeting the mosque) with the Salat al-Istikhara (prayer for guidance), so the two rak'ahs suffice for both. This falls under the issue of combining two acts of worship when one of them is not an end in itself, such as Tahiyyat al-Masjid. Al-Nawawi mentioned that if one supplicates with the Istikhara supplication after a regular Sunnah prayer or other supererogatory prayers, it suffices. It also suffices if one intends both the prayer and Istikhara together.