You can have both sentences.
If you use zitten, it's clear (to me at least) plates and cups are mixed in some box-like environment. If you use staan, all is probably neatly organised in plate stacks in the cupbord, and between two stacks is, so damn! there he left our cup.
Nee. but we don't use "is" very much, it sounds strange, a bit unnatural. Dutch "zitten/staan" for to be has actually always made me think of Spanish "estar" which comes from Latin "stare", to stand, originally. Especially in colloquial (spoken) Dutch, "zitten" is used very often in tye sense of to be somewhere. It often has nothing to do anymore with being seated. Waar ben je? Ik zit in Spanje. The use of staan is a bit more limited, it means to be situated as well, but there is mostly still a concrete connection with being standing: ik sta op de bus te wachten. De beker staat op tafel, etc. But staan has a different similarity with Spanish estar, that zittendoes not have: to be in a state/position: Queen staat op nummer een in de Top2000, Queen has the number one position... Philips staat op winst de afgelopen maanden: Philips is in profit the last few months.
Je kunt "zijn" meestal ook wel gebruiken ipv "zitten/staan/liggen" = "estar", maar het klinkt dan wat onnatuurlijk. In de betekenis van "ser" is het idd "zijn", maar ook "estar" wanneer het een toestand betreft, bv jij bent lerares, jij bent slim, maar ook: jij bent blij. Snap je?
not only, I had more in mind a mug. Mrs Bucket regularly offers one to her neighbour because she tends to get so nervous that always ends up dropping her china. And she always calls these mugs "beaker" (I'm referring to a TV show from the 90s, Keeping Up Appearances)
I was actually thinking more of something like this: http://www.ebay.com/itm/Orginal-Welsh-Beaker-Collie-Mug-/272471014668 or this: http://www.ebay.com/itm/Buckingham-Palace-England-UK-Mug-Beaker-4-5-/110862420901
I tried finding on youtube a video with that specific kind of scene, but I couldn't. But I guess is you just watch any episode as soon as Hyacinth invites Elizabeth to have tea, you'll get to see it. She invariably ends up asking her if she wouldn't rather use a beaker (and offers her what most people would call a mug).
(sorry, I have no idea how to post pictures here :P )
"Our cup? Is more than one person sharing a cup?"
Onze beker can be both singular and plural. Where English almost always uses the plural noun, Dutch often does not when the pronoun is already plural: Was allemaal jullie beker(s) af! = everybody clean your cups! Both beker and bekers is correct here, and beker can also imply that it is one cup shared by several persons. Imagine the situation of a champion football team driving home in the players' bus after winning the cup, just finished a copious dinner with a lot of champagne flowing, one of them shouting in sudden panic: Waar is onze beker?! Oh, hij zit tussen de borden. Other examples: We geven ons paspoort aan de douane = we give our passports to the customs. Ze staken massaal hun diploma in brand = they collectively lit their diplomas. etc. In the last case, the use of the plural diploma's could emply that everyone lit several of their diplomas.