买单 you can say: waiter pay, waiter/ waitress (服务员/服务生)

1. Both买单 and 结账 are ok, maybe 买单 is common in south China and 结账 is common in north China 2. In Chinese, usually we do not distinguish between waiter(多指男服务员) and waitress（女服务员）. if you need normal service, just to say 服务员 is ok, no matter the service person is a man or woman. But if you insist to require a waiter or a waitress, you should say 男服务员 or 女服务员.

In these four words,付钱 ， 付账 ， 买单 ， 计算 买单and付账 are the native expresion,you can also use 付钱，but it's not good enough,and you can't say计算。 the second question: the word waiter or waitress equal to the word"服务员"in chinese. if u still don't completely understand,just comment here and i'm glad to help

买单or结账are not different ! (買單&結帳are traditional Chinese which people in China mainland do not use often) And if you wanna call waiter/waitress, you could say '您好' (means 'hello' usually but 'excuse me' here. And '来' is not polite ) '小姐' is also a common way to call waitress. But in some parts of southern China (like GuangZhou), '小姐' is offensive because it also mean prostitutes

1 付账 = fù-zhàng 2 服务员 = fú-wù-yuán