Step 1: Analyze Statement I:
The statement claims \textit{Plasmodium} secretes histolysin. In parasitology, the enzyme histolysin is specifically associated with the trophozoites of \textit{Entamoeba histolytica}, which use it to dissolve intestinal wall tissues (histolysis). While \textit{Plasmodium} sporozoites do penetrate liver cells, they generally use secretions from their apical complex (like circumsporozoite protein interactions), and "histolysin" is not the standard term used for malarial penetration. Thus, this statement is Incorrect.
Step 2: Analyze Statement II:
Syngamy refers to the fusion of gametes. In \textit{Plasmodium}, this occurs in the stomach of the mosquito vector. The gametes involved are:
Microgamete: Small, motile (flagellated).
Macrogamete: Large, non-motile.
Since the fusing gametes are morphologically distinct, the process is Anisogamy, not Isogamy. Thus, this statement is Incorrect.
Step 3: Analyze Statement III:
\textit{Plasmodium malariae} completes its erythrocytic schizogony cycle every 72 hours. This leads to fever spikes every fourth day (Day 1, Day 4, etc.). This type of malaria is clinically termed Quartan Malaria. Thus, this statement is Correct.
Step 4: Analyze Statement IV:
Quinine, an alkaloid extracted from the bark of the \textit{Cinchona} tree, acts as a blood schizonticide and has been a historical and effective cure for malaria. Thus, this statement is Correct.
Step 5: Conclusion:
Statements I and II are incorrect. This matches Option (D).