Validity:
H-1B1 visas are only valid for one-year increments. However, there is no limit on the number of times it can be issued or renewed. 

Green Card Eligibility:
H-1B1 are single intent visas; therefore, visa holders may not pursue permanent residence while in H-1B1 status. Yet, they may apply for regular H-1B status. Only once they attain this status can they apply for permanent residence.