The faculty handbook detailing issues of leave and sabbatical is here. Assistant professors are considered a "Research Faculty", which is a subclass of "Officer of Instruction".
The policy on inventions and patents can be found at ST&V. Appendix II describes how patent royalties are split.
No special fund in SEAS. There is financial aid available at the School.
Deanna Belcher will be administering the financial aid process again this year. If you have any questions or would like to request a financial aid application package, please contact Deanna at 851-4233, or at dch10@columbia.edu.
There is also something administered through Human Resources called the Primary Tuition Scholarship Program.