I'm not from Texas, but check out the link below (the Texas Code of Criminal Procedure 48.01). It looks like he does, but constrained by the recommendations of the Board of Pardons and Paroles.
Yes, but it's a formality; he can only pardon someone if it has been recommended by the Board of Paroles and Pardons.
A Pardon
There are no time limits set by statute for the granting of a pardon. If you have presented a petition to the Governor's Office requesting a pardon, then it can take as long as the Governor wishes to take in order to consider it.
Yes, the governor has the power to pardon, commute or suspend sentences.
A pardon officially forgives an individual for a crime or crimes. The governor of Maine is the only one who has the power to grant a pardon in the state. To receive a pardon, you must apply for a hearing, and after looking over the case, the governor will make a decision.
The Governor, at his discretion, has the power to issue "pardons."
While Boards or Commissions may exist to advise them on this subject, only the Governor of a state or the President of the US can grant a pardon.
The Texas Government is headed by the state governor. The current incumbent governor of Texas is Rick Perry.
Well not the Reprieves but he has the power to grant Pardons.
Yes. Only the Governor of a state can grant a pardon.
No, that authority has been constitutionally vested in the Georgia State Board of Pardons and Paroles.
This power is granted to the Governor of the state by the state constitution. What anyone thinks of it is immaterial and irrelevant.
No. A pardon cannot be appealed.