Questions on database table and index partitioning in SQL Server
When you partition an index all its data will be split according your partitions.
The partitioning is applied to each particular index independently others.
From the previous point - yes, if you need a partitioned table with partitioned indexes you have to apply the partitioning to the table and each of the indexes.
Too broad to be answered. You could start with SQL Server Table Partitioning: Resources