Is it permissible for me to vow to fast or do anything else as a form of gratitude to Allah Almighty for His guidance?

Thanking Allah for the blessing of guidance and steadfastness is achieved by adhering to His worship and striving in His obedience. Continuous blessings are thanked through acts of worship and obedience, while new blessings are appropriately acknowledged through the prostration of gratitude (sujud ash-shukr). You must safeguard the obligatory prayers, avoid prohibitions, perform supererogatory acts, and constantly praise and glorify Allah. If you vow to perform a specific act of obedience, you are obliged to fulfill it.