dump files maxing C drive with corrupt mdf
You should limit your error log size. According to support, you can accomplish this by executing on the target instance the following script:

USE [master];
GO

EXEC xp_instance_regwrite N'HKEY_LOCAL_MACHINE',
    N'Software\Microsoft\MSSQLServer\MSSQLServer',
    N'ErrorLogSizeInKb', REG_DWORD, 5120;
GO


Another thing you might want to check is where you have your TempDB stored. If it's on C drive, than perhaps you should move it to another drive.

If you'te getting memory minidumps due to crashes of the database engine, than you should follow Dan Guzman's suggestion and create a script to move or delete them.