Standby LED usually green or blue) should be lit when no battery is connected, and charge LED should be flashing briefly. When charging, only charge LED should be lit. And when charge is finished, only standby LED should be lit.
As for CC/CV curve, probably around 4,12V should start lowering current, and keep constant voltage at 4,2V until current drops below 0,1 C, 50mA in your case.
With fuse it would simply start dropping earlier, because TP4056 monitors it's own pin, not battery terminal. In most cases, there is no noticeable difference in voltage, but in your case it will be some (because of mentioned fuse.