Date::Manip is your friend. There's a lot of documentation, yes, but that's a good thing. There are examples that match some of the things you are looking for; here's one I filched from the pod:

perl -MDate::Manip -e '$_ = &UnixDate("Friday in 2 weeks", "%m/%d/%Y")
+; print "$_\n";
[download]

ZZamboni's review offers more examples. Read it over, then ask specific questions if you can't figure out how to do what you want.