Many Replica watches that are highly water-resistant have screw-down crowns. Essentially, the crown of the watch (the knob on the side used to wind and set the watch) screws in place like a tiny bottle cap to make sure that part of the watch is extra water-resistant.
To open the crown, simply turn the crown anti-clockwise to unscrew it (takes about 4 or 5 turns). To close it back, push it in while turning clockwise. Do not close it real tight, just with mildly firm finger pressure. It is the threading that provides water-tightness, so over tightening does nothing to increase the water protection and can overstress the metal, eventually damaging it and ruining the water protection of the crown.
On most mechanical chronographs, yes it is okay. Some people prefer to do this in order to have the large second hand running. There is no evidence this causes any additional wear of any significance to the watch. It also makes little difference in the power reserve on your mechanical Alain Silberstein replique. Omega reports that their watches should lose less than 2% of their power reserve having the chronograph running continuously.
On quartz chronographs it is certainly okay. Though some quartz chronographs may limit the duration that the chronograph will run. Also, some quartz A Lange & Sohne replique may disable the chronograph functions to conserve battery power when the battery is very low.