Scripting?
 

I've never been any good at scripting, so I have this blunt question to ask. Would it be possible or feasible to create a custom movement system that would be for use in a vertical top-scrolling shooter? The type that are most famous from the SNES and Sega Saturn days..

I would actually like to make a simplistic Zelda-type game where the primary and quickest method of transportation is also a vertical shooter, because that would be way more than a solution for the transit problem. Funner and less boring than the boat in Wind Waker and way less lame than warping.

That'd be possible, sure.

Do you think that it would be possible to make bullet-dodging exercises easy for the level designer to implement?
Like make different classes of bullets that would fly across the screen and script it to be simple and flexible to change around.
Also, accuracy of collision detection of the bullets into the player would ultimately be the main focus, trying to get that nailed down accurately.

Accuracy shouldn't be a problem. Coding it in a way that's easy to use (even for level designers) is a design issue.