Compatibilty between GPRS and LTE modules and networks
Lets say we have an LTE module under the coverage of an old base station like 2G with GPRS. Will the LTE module work?


If, and only if, it implements 2G hardware, a fallback on that, and if the network subscription you have with the network operator allows that.


  Lets say we have a GPRS module under the coverage of a newer base station like 4G with LTE. Will the GPRS module work?


No, quite obviously. If it "spoke" 4G, it wouldn't be a 2G modem, would it?