Why does the Torah write "ha'Tzefarde'a" in the singular?
Rashi #1 (citing the Tanchuma): In fact, only one frog emerged from the river, and, when the Egyptians began striking it, hordes of frogs began to swarm from it - the more they hit it, the more frogs emerged - until the whole of Egypt was full of frogs.
Rashi #2: According to the simple explanation, the Torah tends to refer to a swarm in the singular.
In fact, this is the opinion of R. Akiva in Sanhedrin, 67b; according to R. Elazar ben Azaryah there, the frog that came up proceeded to call the frogs from all over to come and plague the Egyptians.
Rashi: As we find later (in Pasuk 13), in connection with the lice.
Why did Hashem initially send only one frog?
Oznayim la'Torah: To give the Egyptians a chance to relent.
See Oznayim la'Torah. Had they done so, the frog would have disappeared. Only they opted to 'put out the fire with oil'