Using JSP Files outside of the Eclipse IDE

I don't know how to extract the JSPs from the IDE, so I can put it in my folder with the HTML pages

Select source file(s) in Eclipse or explorer, hit Ctrl+C, open target folder in explorer, hit Ctrl+V.

Which would bring me into another problem, I want to put the JSPs in an <iframe>, 2 of them make use of <jsp:forward> tags, I'm unsure if all of the forwarding and form submitting will remain within the iframe, because as far as I know <jsp:forward> doesn't have a target attribute, if this is going to be a problem, could anyone point me in the right direction for how to go about this?

It's unclear what you have and what you're struggling with, but all with all this doesn't smell good. It look much like that you're approaching things the wrong way. I'd suggest to start learning servlets. I'd also suggest to develop without <iframe> as long as all pages runs at the same webserver. If you need some kind of head/leftmenu/footer includes, then you should be using server-side includes. JSP offers you the <jsp:include> for this.

Finally, I've only been taught how to the Tomcat server within the IDE, after I've extracted the JSP files from the IDE, how do I run Tomcat independently?

Assuming that you've properly created a dynamic web project, just rightclick it, choose Export > WAR file. Then just drop the obtained WAR file in /webapps folder of Tomcat and start it.