To your question #1 according the the IRC, NO you have to have a railing on the open side of the stairway.
R312.1 Where required. Guards shall be located along
open-sided walking surfaces, including stairs, ramps and landings, that are located more than 30 inches (762 mm) measured
vertically to the floor or grade below at any point within 36
inches (914 mm) horizontally to the edge of the open side.
Insect screening shall not be considered as a guard.
R312.2 Height. Required guards at open-sided walking surfaces, including stairs, porches, balconies or landings, shall be
not less than 36 inches (914 mm) high measured vertically
above the adjacent walking surface, adjacent fixed seating or
the line connecting the leading edges of the treads.
Guards on the open sides of stairs shall have a height
not less than 34 inches (864 mm) measured vertically
froma line connecting the leading edges of the treads.
Where the top of the guard also serves as a handrail on
the open sides of stairs, the top of the guard shall not
be not less than 34 inches (864mm) and notmore than
38 inches (965 mm) measured vertically from a line
connecting the leading edges of the treads.
To your question #2:
There are plenty of handrail kits for sale online and in the big-box stores. Just google "stair rail kit" and you will find many to choose from.