SQL Server - server-side tracing
You'd have to substitute the datetime in the sp_trace_create
That is, drop and create each day unfortunately (as you noted). There is no "alter trace"
Overwritten. The 1, 2, etc suffix is for rollover: not for trace startup
It isn't locked.
The NTFS ownership and permissions are not inherited from the parent folder. You need to change this using Explorer or via scripting (cacls, subinacl) (not sure exactly sorry, been some time)