A.
anwered by: canteau
It looks like the Genesis GS29 uses a Shimano 7-speed drivetrain and you should have no problem with the rear derailleur and shifter working together.
The front derailleur on most department store bikes need the twist shifters micro adjustment action to work properly. The indexed shifting action of the trigger shifter has a defined shift point that might not be able to be achieved with the crankset and front derailleur on the Genesis GS29.