No, Sputnik I reentered the atmosphere and burned up in January 1958.

No, Sputnik 2 reentered the atmosphere and burned up in April 1958.

Yes, Sputnik 3 reentered the atmosphere and burned up in April 1960.

Yes, Sputnik 4 was not launched until May 1960.

Yes, Sputnik 5 was not launched until August 1960

Because the Sputnik program ended with Sputnik 3.

Albeit there was a Sputnik 40 and 41 but these were to commemorate the 40th anniversary of Sputnik 1.

sputnik

No, the Russian's Sputnik was unmanned.

Sputnik was the "family name" for a series of satellites, so there never was a satellite named only Sputnik. They all had numbers with Sputnik 1 being the first.