The best viewers have separate rewinds that can be mounted to a tabletop, allowing plenty of room to access the film for cleaning and cutting. The splicer is the device that actually cuts the film. While it's possible to cut film with scissors or a razor blade, those aren't the best ways if you want two pieces of film to join together properly and go through your projector without trouble. Splicers allow two pieces of film to be aligned on pegs via their sprocket holes. They can be joined together with splicing tape or splicing cement.
Wet splicers use a cement that dissolves the surface of the film.
Some varieties of Super-8 splicing tape are 8mm wide and cover the full width of the film, with sprocket hole openings just like film. Others or not as wide and won't cover the magnetic stripes of sound film. The first style of tape can be used to repair broken or stretched sprocket holes, although your success rate may vary depending on the severity of the damage. Wet splices destroy two frames of film. Dry splices destroy no footage, but poor grades of splicing tape can ooze glue as they age.