'Will you' is more common in modern American English; 'won't you' is also understandable, but it sounds more old fashioned or formal. A British person can confirm, but 'won't you' seems more of a British expression. For the other options, as an American, 'will you' would be preferable; however, for the cup of tea request, 'won't you' seems more natural. Either because tea reminds me of British usage or because it is a different kind of request--rather than asking someone to do something, it's asking if someone will accept your offer of tea.