Goal 3: I would start with the HTML (re: pulldowns etc), you probably require a form in order to sumbit user input to your back-end script. The back-end script can do the calculations and present them back to the webpage. Perhaps you can also present results by constructing an image on-the-fly via Perl (e.g. GD). I can see a bit of a problem when back-end processing takes some time to complete while the webpage says "waiting ...": timeouts, connection failures, exceeding web-host's CPU quota etc. can waste the backend processing and users retrying and clogging the system. I am not sure what a good system for that is: perhaps users submit jobs and when a job is completed an email/pdf is sent to them? Another idea is to add a database caching user requests. You may be able to save some processing this way (on the expense of setting+working a db).
Can you, (or anyone), come up with with a mock-up of this?
Also, I don't know how yet to have mojo projects that live longer than the terminal I have open with a daemon. How do I have a static url like mpj.com/perlmonks/conjunctions or mpj.com/perlmonks/conjunctions.html?