multiple lines in spell abilities - why new paragraph sometimes
The paragraph breaks are only there for clarity. You always do everything the card says, and there's nothing in the game that tries to count how many effects a spell had. That said, Wizards is pretty consistent about doing this for readability, I think in roughly the way you've noted.

Incinerate is all in one paragraph because it's all related; the second sentence wouldn't make any sense without the first. It has a one-shot effect (dealing damage) and also creates a related continuous effect (no regeneration) that lasts until the end of the turn.

Remand does two entirely separate things, so they split it up to make it read more easily. The first part is a one-shot effect (counter the spell) with a related replacement effect (if it's countered, return it to hand instead). The second part is another one-shot effect (draw a card). It would do exactly the same thing if the paragraph break were removed, though - and in fact, if it were the effect of an activated ability on a permanent instead of a spell on its own, it would presumably be written as one paragraph.

The instructions you follow while resolving an instant or sorcery are spell abilities (112.3a), so in combination with 112.2c, I believe that technically means that Incinerate has one spell ability and Remand has two. I can't think of anything in the rules or the game that actually cares about that fact, though. The rules really only even mention spell abilities in a couple places where they need a phrase to specify that something is part of resolving a spell, like the first part of Cipher (the part that lets you encode the spell). Splitting abilities on paragraph breaks is far more important on permanents, where they might be activated or triggered abilities that really need to be clearly delineated. For example, on Dragon Tempest, it's important that the two paragraphs are separate abilities!

Yes, linked abilities do exist, and two linked abilities are often put in multiple paragraphs (like Oblivion Ring). But the paragraph break isn't what makes something a linked ability. There are a variety of things that indicate a linked ability (e.g. "cards exiled with X") but only one mentions paragraph breaks and in fact requires them to be in the same paragraph to be linked (static abilities and triggered abilities in the same paragraph are linked). There's none of that going on here.