I'm in a multi-storey flat too. You can have a washing machine - mine connects via the same plumbing as the sink, rather than a separate standpipe, in the kitchen. But my b****y neighbour upstairs does her washing overnight 'to save on electricity'. Argggh. I do mine before 8pm to prevent annoying the guy below me.
Post is a bit more complicated. Some flats have post boxes at the entrance, but my post comes straight to my front door. Unfortunately, the post office just has one key to get into our communal areas, which means some days, if the posties haven't passed the key on, we don't get our post. It also means we can't get courier parcels (TNT etc) cos they can't get access, even to drop a card off - so with ebay etc I make sure the items are sent by Royal Mail or direct to my place of work or parents' house. But it does mean getting post dropped off is very secure.
Hope this answers your questions.