How to know the statistics are up to date, is there any way to find when the last statistics were calculated?
Do I need to just look at the stale_stats and last_analyzed column of the dba_tab_statistics view?
You can find this in the XXX_TABLES views (e.g. DBA_TABLES, USER_TABLES, ALL_TABLES). The column you're looking for is LAST_ANALYZED, so for example
SELECT OWNER, TABLE_NAME, LAST_ANALYZED
FROM USER_TABLES