Do you think schools should do more to encourage students into doing scientific research?

Enquiry based learning is part of ensuring relevant, meaningful and fulfilling learning experiences,  so yes, absolutely; I support schools which encourage students' scientific research. 

Sure, and earlier best, since kids are eager to learn new skills 

Yes, schools need to do more via teachers. Teachers them selves need to show the beauty and interest of study and scientific research and must be very honest. Then school students will be motivated and do well