If the “Replserv” service is needed to be stopped and restarted, could it be done safely when the application is running without causing any complications to DataExchange and more importantly causing corruption to the application database files? Similar question also to using DEACT and DXACT when the application is up. I wish to minimize the down time on the application as much as possible.

There is no problem with corruption to the application database, but if you stop "Replserv", DATAEXCHANGE don't see changes in this time frame, so your replica could be out of sync (same as dxact/dxdeact).