Questions about index, stats on custom schemas and APEX

We are in the process of upgrading our EBS application from 12.1.3 to 12.2.10. To support live patching, we have to use the APPS schema and the synonyms and not refer to the base tables. I have questions about handling indexes, and gathering stats.

• Some of our batch processes drop indexes and recreate them as part of the process. Do we create indexes against the base table or synonyms?
• Some of our programs gather statistics as part of the batch processing. For example, here is one. 

EXECUTE DBMS_STATS.GATHER_TABLE_STATS('SIUFIN','SIUGL_FYE_FO_HEADERS_T');

Do I keep the schema name as they are (custom schemas where the base tables belong) or do I have to change them to APPS?