When should cyclists use pedestrian facilities?
In most cases it's a matter of common sense and good judgement. 

If the pavement between the road and the bike racks is quiet and you're not going to impede anyone, cycle it. Same for the bike path not directly accessed from the road. 

Your 3rd point, though is the crux of many discussions and we should be careful in how to answer it here. My perspective, although it's not clear whether this is the (UK) legal situation, but just how I 'morally' feel, is that if you approach the junction on a bike you shouldn't confuse the situation by morphing into a pedestrian and pushing your bike through the junction, then remounting your bike. While this might seem expedient it is reinforcing the view of other road users that you're somehow less than a proper road user, if you can use other facilities, then you should all the time, says that argument. 

Certainly there are some intersections where it might be safer to do so, but the law (and cyclists' reputations) are often contrary to safety. It's a tricky question and common sense is often not to the fore in confrontations. 

I try to avoid any use of the pavement unless it is explicitly marked as shared use, but where it's not clear, to try to not do things that would blatantly and needlessly annoy others. After all, cyclists in many locales have a bad reputation for selfish behaviour, I'd rather not add to it.