You could always create some tasks and see what happens...

But in short, the due date affects how the task is shown, sorting order, font etc but it will still be visible.

Well, there's no inherent support for a "project" item, just tasks. You can certainly use tags to mark tasks with something to distinguish them as belonging to a project. For example, I will create a project name tag with a prefix of "-" so for example I could have -holidays and tasks using that tag would be buy holiday cards, come up with ideas for presents, plan trip to see family, etc. Each one of these gets its own due date. If you set a given task as due within two weeks, you should see it unless you are specifically hiding it. In other words, if you don't filter your smartlist to only show you tasks that are due sooner than two weeks from now (or later), then those tasks should show up until they are completed.

Don't be nervous about this stuff, just try it out! You can't break RTM! Whenever I'm in doubt about how something works, I just create a task and see if it shows up the way I expect. Sometimes I'll even change certain characteristics like the due date, a tag, etc., and that will give me further evidence of whether I'm going to get the expected results. If it doesn't work the way you want, you can always just delete it and try something else later. In other words, trying things out on your own will solve a lot of worrying and asking people here when you can quickly determine the answer for yourself.