Yup. Lots of ways.
Extended events, SQL Audit, DDL triggers are just some of the options

I'd start by looking for jobs that run every hour, starting at 00:45. Shouldn't be a lot of them.

Yes.
You probably want to use EXISTS and/or NOT EXISTS. Since you have to check multiple rows for each row, doing this needs a subquery. One used with either...

Yes, it...

Well, obviously it is, or the report you mentioned above would have...

You probably want to use EXISTS and/or NOT EXISTS

Bet coffee that he's looking at the wrong...

Default trace doesn't go back far. It's not a full history.

Still, SQL doesn't revert changes. If the objects are an older version, either someone reverted them, or you're...

You can't fix that.
If you do recover the DB and run checkDB, you can't get it back into restoring state, and without running checkDB, it won't come out...

Either the database was restored to an earlier version, or someone ran ALTER scripts (or DROP & CREATE) on all of the affected objects.

Check restore history, check the...

You can do a dynamic sort without dynamic SQL. Not going to be fast, but that's the price you pay for such code.

ORDER BY
CASE @Ordering WHEN...

The distinct is still completely unnecessary, as there is no way whatsoever that a TOP(1) could return duplicate rows.

That said, removing the DISTINCT will not change the query's...

SQL Server: Transactions\Transactions/sec, then select TempDB only.

The key indicator that it's not an error from SQL Server is that it's a .net exception. SQL Server is not written in .net, and won't throw .net exceptions