Wait. Do not restart SQL (the roll back will just continue with the DB unavailable). Check what the shrink process is waiting for.

Do not kill the process from Windows. There's an MSDN blog somewhere (will find when I get home if you like) that discusses what can happen in that case and...

Why are you partitioning? What's the intended goal?

If you want to drop an index at the subscriber, go to the subscriber and drop the index. Make sure that you don't adversely affect the subscriber's workload by doing...

Unless the database is in full recovery and there was a full backup taken at some point prior to the delete, there won't be anything in the log to analyse.

Please post table definition, index definitions and execution plan as per http://www.sqlservercentral.com/articles/SQLServerCentral/66909/

That's how the index rebuild is executed behind the scenes

Possibly related to this

http://www.sqlskills.com/blogs/jonathan/dbcc-checkdb-execution-memory-grants-not-quite-what-you-expect/

Why is the log growing? Logs should reach a steady spot where they don't grow any further, so what is causing your log to grow continuously?

Did you read the articles?

Any suggestions on exactly what specifically (since the articles explain log reuse and reasons why it might not be reused)?

If you have this problem, open a case with CSS. Data purity errors should not ever happen in the system tables.

Unless you have a really good reason otherwise, leave min server memory at default. 14.25GB is a little high on a 16 GB box. I'd usually start at 12...

By restoring a clean backup. Repair is usually a...

That support article explains how to fix the error in user tables. The table in question...

Let me guess, the index is 4 pages in size (at the leaf level)?