What should one do if they are absentminded in their prayer and do not know how many rak'ahs they have prayed or whether they recited Al-Fatihah, given that their prayer is fast?

You must seek Allah's help and take care of your prayer by perfecting your purification and performing wudu thoroughly, and by offering the obligatory prayers with tranquility and devotion, and by striving against your own self to feel the greatness of standing before Allah and conversing with Him. If you doubt whether you have prayed two or three rak'ahs, then base it on the lesser number and perform the prostration of forgetfulness (sujud as-sahw). As for performing the prayer quickly, there is no harm in it as long as it does not compromise tranquility.