All permanent residents are required to have valid GC in possession at all times. GC are granted for 2(conditional) or 10 years. Before expiration they must be renewed. Person who is absent from US for period longer than 1 year must obtain re-entry permit before arrival because they may be deemed to abandon their residency in the US. As a general rule, permanent residents are allow to freely travel, make trips outside the country, but such trips should not be longer than 1 year. However if you are planning to be absent from the country for longer than 1 year, such person should apply for re-entry permit ( form I-131). However Form I-131 is not a guarantee for re-entrance because absent person first must be determined admissible. If you stay outside the country for more than 2 years, it is advisable to apply for returning resident visa at US Embassy or Consular abroad.
GC holders are not allow to vote in the federal, state or local elections. However, there are few jurisdictions where permanent residents may vote.