They are represented in collective bargaining and contract stewardship issues, they have access to representation in cases of discipline or dismissal, and they can file greivances the same as a full member. The % they pay represents the % that covers these costs only. There's a formula every local union uses at the end of the year to determine the Beck Assessment (aka Agency Fee) as compared to to a full dues paying member.
As far as voting, no, non-members do not have the rights of a union member at union meetings. As far as whether or not they vote with their bargaining unit in contract ratification, I can't remember whether they do or not. When I was doing Business Rep and negotiations for my union, I never had to have a contract ratified that represented any Beck Objectors. My Local only has three that I know of.