Step 1: Set the scene.
Plasmodium is the malaria parasite with a two-host life cycle, part in humans and part in the female Anopheles mosquito.
Step 2: Recall the human phase.
Inside humans, sporozoites multiply asexually in liver cells, then enter red blood cells (RBCs) and again multiply asexually, releasing merozoites.
Step 3: Recall where gametocytes form.
The sexual forms, the gametocytes, develop inside human RBCs, not in the mosquito. So option (4) is wrong.
Step 4: Recall the mosquito phase.
When the mosquito bites and takes blood, the gametocytes mature into gametes inside the mosquito gut, and fertilization happens there.
Step 5: Test each option.
Reproduction in liver cells and in RBCs is asexual, so options (2) and (3) are wrong. Fertilization in the mosquito gut matches the actual cycle.
Step 6: Conclude.
The correct statement is that fertilization takes place in the mosquito gut, which is option (1).
\[ \boxed{\text{Fertilization takes place in mosquito gut}} \]