Hmm... are you sure you found the largest possible font size for questions? 
Quickly to your questions:
SAP HANA doesn't support function based indexes (FBI). Instead you can create generated columns (GENERATED ALWAYS AS - check the SQL reference for the exact syntax). These generated columns are semantically the same as FBIs
And indexes are always local to a partition.
All in all the most important thing about indexes in SAP HANA is that you really should not make the mistake and apply your Oracle-Knowledge of indexes to SAP HANA.
Although indexes are not completely irrelevant in SAP HANA they are way less important and required than e.g. in Oracle.
I've described indexes in SAP HANA in Richard's and my book (Book Announcement: SAP HANA Administration) in some more detail.
- Lars