Does the reward multiply with the multiplicity of intentions for the same act, such as praying the two rak'ahs of Fajr with the intention of earning its reward, as well as the reward for the sunnah of ablution and greeting the mosque?

Yes, the reward is multiplied by the multiplicity of intentions in a single act. So, whoever enters the mosque in a state of purity (wudu') and prays two rak'ahs with the intention of the Fajr Sunnah, the Wudu' Sunnah, and Tahiyyat al-Masjid (greeting the mosque), will receive the reward for all that he intended. Al-Nawawi mentioned that whoever intends by a prayer both the obligatory prayer and Tahiyyat al-Masjid, his prayer is valid, and he achieves both. Al-Ghazali clarified that the multiplication of virtue occurs through the abundance of good intentions. A single act of obedience can accommodate many intentions. He exemplified this with sitting in the mosque, which can have multiple intentions such as visiting Allah, awaiting prayer, restraining one's limbs, dedicating one's thoughts to Allah, remembering Allah, benefiting from knowledge, or seeking a brother for the sake of Allah, among others. In this way, good deeds are multiplied, and actions are purified. Ibn Baz affirmed this principle, for Allah's grace is vast.