Statement 1 is incorrect: Governor cannot pardon a death sentence. 

Statement 2 is correct 

Pardoning Power of Governor: 

• Under Article 161, the Governor shall have the power to grant pardons, reprieves, respites, or remissions of punishment or to suspend, remit or commute the sentence of any person. But the person should be convicted of any offence against any law which is under the executive power of the State. 
• Exceptions: 

• The Governor cannot pardon the death sentence (the President has the power to do so). But the Governor can suspend, remit or commute the death sentence. 
• The Governor cannot grant pardon, reprieve, respite, suspension, remission, or commutation in respect to punishment or sentence by a court-martial. However, the President can do so. 

Source: Article