Table 'craft.craft_elementindexsettings' doesn't exist
This issue has actually come up before in the Slack channel...


  "That’s a brand new Craft 2.5 table, so you’ve probably tried to do the update before, it failed and you didn’t clear out all tables from the database when you retried." - Brad Bell


As you mentioned, your auto-update did not complete successfully. So the logical next step (as you tried) is to perform a manual update.

But here's the catch... Before you made your 2nd (manual) attempt, you didn't roll back your database. Between attempts, you would need to drop all tables and re-import your original database SQL file.