Learn English – correct way of cooking

When used in this way, said is normally preceded by the. The definite article is, however, sometimes omitted, as in your examples. When a word is omitted, but can be retrieved from a previous part of the text, the feature is known as ‘ellipsis’. In the case of said, it probably occurs mostly in speech, rather than in formal prose, and may sometimes be intended to be amusing. My personal view is that said as used in this way, with or without the, is best avoided. It rarely adds anything useful and almost has the status of a cliché.

They are both correct. If the focus is on the fact that I now have two objects, whereas before I had only one, I'd say split in two; if I want to stress that now each object is half the size of the single object I had before, I'd say split in half. In each case, though, the emphasis is so subtle that it would probably escape the conscious perception of the hearer, as indeed, the stress probably was not consciously calculated by the speaker.