answers in line...

1)  Can I upgrade from 8.0.3 directly to 9.0.2, or do I have to first upgrade to 9.0.0, then 9.0.1, then 9.0.2?

You can go directly to 9.0.2

2)  Are there any gotchas or difficulties with using the Server Settings Migration Wizard to migrate and upgrade to EV10 concurrently?  I know the stated requirement is that the target EV version has to be the same or greater than the source, but I'm wondering if it would be easier to use the SSMW to migrate 9.0.2 to the new hardware first, then do an in-place upgrade to 10.  If anyone has any experience / feedback either way, it would really be helpful.

I have used the Server Settings Migration many times without issue.  Works great and I would go straight to 10. 

3)  What about the new 64-bit index?  Do I need to mount a separate index volume on the new server for the 64-bit index?  Or will it create the new index for the newly injested data on the same volume as the existing 32-bit index?

No need to mount a new volume, 64-bit indexes will be created automatically

4)  The current EV databases are SQL Server 2005 (on the EV server).  For the new server I want to upgrade to SQL Server 2008 R2 (on the EV10 server).  If I detach the database volumes from the old server and attach them to the new server (they're on SAN storage), will the databases be automatically upgraded when the EV directory and storage services start up for the first time?  Or do I have to perform a manual move of the databases?

Just follow this technote and you should be golden:

How to move the Enterprise Vault (EV) SQL databases from one SQL server to another.