Yes, It can invest into FD Scheme of Private Company.
You need to have all sanctions / permissions from the Trust to invest the money.
The Company should be CRISIL / ICRA / CARE / Fitch / S& P accreditated coompany.
Higher the ratings of the company, it will more safe & secured to invesments.
Kepp FD for 1 year and see how they give service, then think on long term investments.