Step 1: Analyze statement I.
Nana Saheb was the adopted son of Peshwa Baji Rao II but was not officially recognized as his successor by the British. Hence, statement I is incorrect.
Step 2: Analyze statement II.
Nana Saheb played a major role in the Revolt of 1857 and led the uprising at Kanpur. Hence, statement II is correct.
Step 3: Analyze statement III.
The rebellion of Nana Saheb did not collapse at the beginning of 1857; rather, it continued for some time during the revolt. Hence, statement III is incorrect.
Step 4: Analyze statement IV.
After the failure of the revolt, Nana Saheb is believed to have escaped to Nepal. Hence, statement IV is correct.
Step 5: Conclusion.
Thus, only statements II and IV are correct.
Final Answer: Only II and IV are correct.