Creating content regarding to node address arguments Say it I have such node alias:
example.com/content/my-fancy-page/

If user enters to node above, he will see default page content of my fancy page.
After some process I will redirect him to this:
example.com/content/my-fancy-page/tt3741/
or this
example.com/content/my-fancy-page/tt3802/


Regarding to user's selection he will see the "tt3741" or "tt3802" content that resides inside database. Is it possible to do this with hooking etc. When I try "example.com/content/some-old-page/foobar" in my old website I get 404 error. So is it nt possible?
Is it possible to cache these three addresses seperately with Boost module? Or Boost only caches "/my-fancy-page/"
Path aliases must be exact, thus if you want my-fancy-page/tt3741 to work you need to create an alias for it. If you link to the node path node/6 then node/6/tt341 will work. This has to do with how hook_menu works vs how path aliases work.

If you wish to hack around how path aliases work you can try out the PURL's Path Extensions feature http://drupal.org/project/purl or use hook_url_inbound_alter() to get the correct node given the unique alias. 

Boost will work as long as each URL is unique (same as drupal's core cache). Good luck.