Might I suggest that you wait and find out just how much actual damage has been caused before you start borrowing trouble ?

I've known engines to run with little coolant for considerable distances without any long-term ill effects. In terms of repair, I'd imagine you're pretty well covered. A car (whether new or used) should be 'fit for purpose', so any reputable garage will ensure that you are not left facing a bill for this.

In terms of regularly checking the coolant - well, you've only had the car a fortnight. If they put a condition on the warranty that you HAD to check it every week or 2 weeks, I'd imagine it would be thrown out as an unreasonable (and thus unfair and unenforceable) condition.

As to what you're going to be entitled to ... the simple answer is to be put back into the position that you were in beforehand. That MIGHT mean a new engine (if the old one is utterly goosed), but it might also just mean that it gets refilled with coolant and leak tested IF there are no other problems with the engine.

The critical thing, if they do that, is to make absolutely certain that you get down from the garage, on paper, what the problem was, what caused it, and the fix that was applied. That way, if it fails again (or if something serious goes wrong in a few months) you've got some ammunition as to previous faults, and the possibility of the new fault being aused by the old fault.