Since Luffy's body is made of rubber, can small cut wounds/gashes seal like rubber in the real world would normally do? Or do they heal like normal skin?
Not actually rubber. Luffy's devil fruit is not really the Gum-Gum Fruit, but
the Hito-Hito (i.e. Human-Human) fruit model Nika, which gives him the ability to manipulate his body however he can imagine, and upon awakening, also the surroundings.
So, this question is no longer valid.
As terrible of an idea it would be for him to heal like rubber since it doesn't heal at all, Luffy heals like a human. Remember, Luffy is like rubber, He isn't rubber though. He's still skin and bones. If he was like rubber, Luffy would not sink in water. But he still has the density of a human. Or maybe it's the fact that he turns completely human when touched by rubber.