Is it against normal form to include columns with date parts if there is a datetime column in the same table?
It is against either 2nd or 3rd normal form, depending on whether the datetime column is part of the key.  

You could be harmed by an update anomaly if you change a batch date, but forget to change one of the fields that are derived from it.  Now the database is self cntradictory.

When I was faced with this, I adopted an alternative approach.  I created a table called almanac, with a date type key, and all those other fields like weekday, fiscal quarter, and so on.  I then wrote a program to fill this table with ten years worth of dates.  Then, whenever I wanted all those fields with respect to any date, I just did a join.  This was especially useful because fiscal quarter was a company defined attribute, and wasn't in any built in function.  We had dozens of date fields, and reporting by fiscal quarter was a requirement.