I'm sure new spell creations do have to be registered by the Ministry. However, Sectumsempra and the like are dark spells, and of course they wouldn't be Ministry-approved. So of course he wouldn't register them. Sort of like the Marauders not being registered animagi.

On the subject of creating a spell, I would think it would be something like creating a new chemical equation to make an entirely new substance. It would require a lot of thought, and knowledge of Latin to create the root of the word, and then...this is where I am out of my element. I have no idea after that.