Greenstone.Walker
Adventurer
Not sure what you mean but there are plenty of slashing weapons that are one-handed and there are plenty of slashing weapons that are two-handed.
No, there aren't.
D&D has 10 slashing weapons. Four are light (handaxe, sickle, scimitar, whip), two are versatile (longsword, battleaxe), four are heavy (greataxe, greatsword, glaive, halberd). Nothing in the two-handed non-heavy category, nothing in the one-handed non-light category. The other two damage types both have weapons in both of those categories.