If I get a teaching certificate in Secondary education, would I be able to teach elementary school?

check the student counseling office at your school for requirements.

It depends on your educational jurisdiction.  Here in Ontario an Elementary Teacher's Certificate gives qualifications in Primary, Junior, Intermediate; a Secondary Teacher's Certificate gives qualifications in Intermediate, Senior. While it is possible for a teacher with Senior and Intermediate qualifications to teach  K - gr 8 students preference would be given to those who have Primary and Junior qualifications. That being said the Ministry of Education does offer additional qualification courses for teachers so it is possible for a secondary school teacher to be qualified in Primary and Junior. 

That depends on the licensure requirements where you live, but I would hope not. Teaching children is very different from teaching adolescents. It's not just about know the subject matter. Children in grades k-3, for example, typically sit in groups at tables, do groupwork and do a great deal of hands on, interactive activities. That's how children that age learn. That's very different from teaching secondary students. You need to know a lot of different things, such as classroom management, motivation, spotting learning disabilities and what to do about them, etc.