I've an HTTP server that is within our internal network and accessible only from the inside it. I must put another server that will pay attention to an HTTPS port accessible from outdoors, and forward the demands to that particular HTTP server (and send back the reactions via HTTPS). I understand that you will find a number of ways to get this done with a few programming involved (and that i myself designed a temporary solution with Tomcat and a simple servlet I authored), but it is possible to method of doing exactly the same just inserting parts already made (like Apache + modules)?

This is actually the kind of use-situation that stunnel is made for. There's a particular example of utilizing stunnel to wrap an HTTP server.

You should look at whether this is actually advisable, though. Web programs created for use in the corporate firewall are frequently fairly poor about security. Basically encrypting the connections prevents casual eavesdropping, but doesn't secure the website. If the attacker finds your outward facing server and begins hooking up into it, they are able to still try to look for exploitable defects within the web service (SQL injection, mix-site scripting, etc).

With Apache consider mod_proxy.

Apache 2.2 mod_proxy docs

Apache 2.0 mod_proxy docs