What should a Muslim do if the Imam of the Tarawih prayer prays four rak'ahs at a time, and is he permitted to follow him or should he pray at home, and will he be credited with praying an entire night if he prays twenty rak'ahs? And what is the time for abstaining from food and for the Fajr prayer if the call to Fajr prayer (adhan) is at 3:22 and the iqamah (call to commence prayer) in the mosque is after 4:30?

The Sunnah in Tarawih prayer is to perform Taslim (salutation) after every two rak'ahs. The Imam's prayer is valid if he does what is permissible according to some scholars, and the worshiper is obligated to follow him. Your prayer in the mosque with the Imam is better. As for the difference in the time of the Fajr adhan in Turkey before Ramadan compared to its time during Ramadan, the reason is that they delay the adhan throughout the year to achieve 'isfar' (lightening) for the Fajr prayer, and they call the adhan at the true time of Fajr during Ramadan for 'imsak' (abstinence). Therefore, it is obligatory to stop eating at the time of the adhan and to pray with the congregation.