Well, you have listed down all the stuff that you want to use and their purposes either. But I just have one suggestion that if you are using a GPS module then you actually do not require an RTC, IMO. Because you can get the timing information from the GPS as well. Further, you must be aware that prayer timings change throughout the year. For which, I hope you can find the time map in some sort of excel or text file which you can use to play Azan audio at the right time. But these timings also change with position. So if you can keep yourself restricted to certain places then this project could be more practical. Otherwise you will have to maintain different text files for time map for different regions.
Else you can consider using SBC (Single Board Computer) which is a credit card sized computer, on which you can connect ethernet and get these informations over internet and play the Azan audio as required.
Hope that helps.
Thanks.
MSBR