Are universities allowed to ask you where else you're applying? It doesnt seem to make any sense why they'd need to know... Do I have to answer, will it affect my application if i just ignore the question?

It's something I find quite baffling, with undergrad applications it was all via UCAS and they had no (legitimate) way of finding out.

God I cant even remember what I had written in answer...
well, they wouldnt 'officially' have any way to find out, nor would anyone have the time or reason to find out, unless they had special reasons.

if a candidates really good, univs will want to keep the person and hence make an offer, if they can, and then names of other schools wouldnt make much of a difference.

This is highly open to perception actually!