Кевин, in this particular sentence, it is preferable to agree the verb with много formally, i.e. singular: На столе стоит много чашек. However, in the modern Russian both options could be correct (agreeing formally and putting verbs into singular or agreeing by the meaning and putting the verb in plural). You can read more about it here: http://new.gramota.ru/spravka/letters/22-spravka/letters/64-bolshinstvo. If there were more words between много чашек and the verb, it could be plural: Много фарфоровых чашек, наполненных до краёв душистым чаем, стояли на столе. I would suggest to use singular in most cases, because it is safer. P.S.: Mind the spelling: стOять

На столе стоят чашки. Но: На столе стоит много чашек.

Great question! "На столе стоит много чашек" is correct even though it sounds strange.

можно говорить и так и так. ошибки не будет)

Es wird richtig sein: На столе стоит много чашек. Aber in der gewöhnlichen Unterhaltung können beide Versionen zu hören.