What are the pros/cons of splitting date and time into separate fields vs. using the datetime data type and storing the date in a single field?
For reporting purposes splitting the field out into date and time has some benefits.  Some possible benefits you could realise include:


You can make a date reference table (much the same as a date dimension in a data warehouse) with your breakdown into weeks, months etc.  This can be keyed on the date and used with a join.
Analysis by time of day is easier with a separate time field.  You can also round the time to an appropriate grain and make a reference table.
The index would be slightly narrower although each leaf row still has a (IIRC) 6 byte page reference, so it's not such a great saving overall.


For your application you might get a win from a date reference table (make a clustered PK on date for efficient lookup), which will probably be more efficient than de-normalising the week and month onto your large table.