You could make a fight for your "rights" (which you did lose when you were convicted). You will end up no longer on probation and wishing you were back outside of the prison system.
Bottom line is they can do pretty much as they wish. Some are rougher then others.
Yes, a probation officer typically needs a warrant to access a probationer's email, as it is considered private electronic communication protected by the Fourth Amendment. Probation officers may also have legal means to request access through a court order or the probation agreement itself.