Yes, they do mean the same, but they're not always used in the same way. 'What are you doing?' is a simple request for information. Without any further context, it means refers to what someone is engaged in at that particular moment. It can sometimes appear a little 'bare' as a question - maybe rude or too direct. 'What are you up to?' is a more informal, conversational question, which can also mean 'Tell me about your life at the moment - what's good? what's bad? what's happening?' . You would often meet a friend or acquaintance whom you haven't seen for a while and say: 'So, what are you up to these days?' It's a fairly open question, and an invitation for them to give you their news. You can also use it in the present perfect : 'So, what have you been up to recently?'

A very casual way of saying this expression would be : What's up? (More to be used with very close friends)

yes :D

Yes, but it is a more casual way of asking.

As a native speaker, I say "What are you up to?" more often than "What are you doing?".