1.Is JSP "dead" in favor of JSF?
In the realm of JAVA EE JSP is announced "obsolete". In a wider world it is well alive.
2.Is Java EE the platform JSF runs on top of or something different altogether?
Depends on where is the "top". Servlets are the basement for most Java frameworks including JSF.
3.Is JSF merely an MVC framework for developing web applications?
Yes, it the sense that JSF is a presentation layer framework.
4.Is JSF a framework developed by Oracle and part of Java, or is it a separate framework altogether (Much like the Zend Framwork is from
PHP)?
JSF is an official part of Java EE 7 by Oracle.
5.[Bonus] Would you recommend learning jsp or jsf?
Both, to a certain depth. Consider also HybridJava - its is same powerful as JSF but about twice simpler.